## Can a parabola have only one x-intercept?

Your browser seems to have Javascript disabled. We're sorry, but in order to log in and use all the features of this website, you will need to enable JavaScript in your browser.

When we graphed linear equations, we often used the x — and y -intercepts to help us graph the lines. Finding the coordinates of the intercepts will help us to graph parabolas, too. We will use the decimal approximations of the x-intercepts, so that we can locate these points on the graph. The graphs of these equations are parabolas. Earlier, we saw that quadratic equations have 2, 1, or 0 solutions.

The graphs below show examples of parabolas for these three cases. Since the solutions of the equations give the x -intercepts of the graphs, the number of x -intercepts is the same as the number of solutions.

Now, we can use the discriminant to tell us how many x -intercepts there are on the graph. Before you start solving the quadratic equation to find the values of the x -intercepts, you may want to evaluate the discriminant so you know how many solutions to expect.

Don't want to keep filling in name and email whenever you want to comment? Register or login to make commenting easier. Save my name, email, and website in this browser for the next time I comment.

### predicting x-intercepts

Search Log In. Finding the Intercepts of a Parabola. To do 6 min read. Use the zero product property. This quadratic does not factor, so we use the Quadratic Formula. Solve by factoring. Find the value of the discriminant to predict the number of solutions and so x -intercepts. There are no x -intercepts. So there is one x -intercept. Solve the equation by factoring the perfect square trinomial.

Use the Zero Product Property. Solve for x. Share Thoughts. Finding the Axis of Symmetry and Vertex of a Parabola.Get a free answer to a quick problem. Most questions answered within 4 hours. Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. Quadratic Formula. The graph of a quadratic function can have 0, 1 or 2 x-intercepts.

How can you predict the number of x-intercepts without drawing the graph or completely solving an equation? Add comment. The graph of a quadratic equation is always a parabola. The x-intercepts are the points where the parabola crosses the x-axis. Will a parabola always cross the x-axis? Picture a parabola that opens upward. If its vertex lies above the x-axis, the parabola will never cross the x-axis. Hence it will have no x-intercepts. Similarly, if the parabola opens downwards inverted and its vertex lies below the x-axis, it will never cross the x-axis.

### The graph of y = ax^2 + bx + c

So to figure out whether a quadratic equation has 2, 1, or no solutions, you need to know two things: 1 the y-coordinate of the vertex and whether the parabola opens up or down inverted. Plug that into the quadratic equation to get the y-coordinate of the vertex y vertex. Whether the parabola opens up or down depends on the sign of athe coefficient of the x 2 term.

Ask a question for free Get a free answer to a quick problem. Find an Online Tutor Now Choose an expert and meet online.The graph of a quadratic function is a parabola. Before tackling the subject of the x-intercept, students should be able to confidently plot ordered pairs on a Cartesian Plane. X-intercepts are also called zeros, roots, solutions, or solution sets. There are four methods for finding x-intercepts: the quadratic formulafactoring, completing the squareand graphing. Use your finger to trace the green parabola in the image in the next section. Notice that your finger touches the x-axis at -3,0 and 4,0.

Therefore, the x -intercepts are -3,0 and 4,0. Note that the x-intercepts are not merely -3 and 4. The answer should be an ordered pair. Note also that the y-value of these points is always zero. Use your finger to trace the blue parabola in the image in this section. Notice that your finger touches the x-axis at 3,0. Therefore, the x-intercept is 3,0. A question to ask to check your understanding is, "When a parabola has only one x-intercept, is the vertex always the x-intercept?

Use your finger to trace the blue parabola in this section. Note that your finger does not touch the x-axis. Therefore, this parabola has no x-intercepts. Share Flipboard Email. Jennifer Ledwith. Math Expert.

Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics. Updated October 26, The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate. A rule of thumb reminds us that when we have a positive symbol before x 2 we get a happy expression on the graph and a negative symbol renders a sad expression. The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry.

The axis of symmetry has the equation. When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points. If you have an absolute value of a that is greater than 1 the parabola will be narrower than the parental quadratic function. And the opposite that if you have a absolute value of a that is less than 1 then the parabola will be wider than the parental quadratic function.

Here you can get a visual of your quadratic equations. All quadratic functions has a U-shaped graph called a parabola. Use both positive and negative values! Share on Facebook. Search Pre-Algebra All courses. All courses. Algebra 1 Discovering expressions, equations and functions Overview Expressions and variables Operations in the right order Composing expressions Composing equations and inequalities Representing functions as rules and graphs.

Algebra 1 Exploring real numbers Overview Integers and rational numbers Calculating with real numbers The Distributive property Square roots. Algebra 1 How to solve linear equations Overview Properties of equalities Fundamentals in solving equations in one or more steps Ratios and proportions and how to solve them Similar figures Calculating with percents. Algebra 1 Visualizing linear functions Overview The coordinate plane Linear equations in the coordinate plane The slope of a linear function The slope-intercept form of a linear equation.

Algebra 1 Formulating linear equations Overview Writing linear equations using the slope-intercept form Writing linear equations using the point-slope form and the standard form Parallel and perpendicular lines Scatter plots and linear models. Algebra 1 Linear inequalitites Overview Solving linear inequalities Solving compound inequalities Solving absolute value equations and inequalities Linear inequalities in two variables.

Algebra 1 Systems of linear equations and inequalities Overview Graphing linear systems The substitution method for solving linear systems The elimination method for solving linear systems Systems of linear inequalities.

Algebra 1 Exponents and exponential functions Overview Properties of exponents Scientific notation Exponential growth functions.

Finding the y-intercept of a Quadratic Function

Algebra 1 Radical expressions Overview The graph of a radical function Simplify radical expressions Radical equations The Pythagorean Theorem The distance and midpoint formulas. Algebra 1 Rational expressions Overview Simplify rational expression Multiply rational expressions Division of polynomials Add and subtract rational expressions Solving rational expressions.No, if the vertex of the parabola is 0, 0 it will only have one x intercept.

The parabola might have zero x intercepts as well. If the discriminant, b2 - 4ac is less than zero, y has no real roots. This means that there is no real value of x for which y equals zero and so the parabola has no x intercepts.

If the discriminant is greater than zero, there are two distinct intercepts. If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts. The zeros of functions are the solutions of the functions when finding where a parabola intercepts the x-axis, hence the other names: roots and x-intercepts.

I think you are talking about the x-intercepts. These will be the "roots" of the parabola. A parabola is a type of graph that is not linear, and mostly curved. A parabola has the "x squared" sign in it's equation.

A parabola is not only curved, but all the symmetrical. The symmetrical point, the middle of the parabola is called the vertex. You can graph this graph with the vertex, x-intercepts and a y-intercept. A parabola that has a positive x squared would be a smile parabola, and the one with the negative x squared would be a frown parabola.

Then you can solve for the x-values by any number of ways: Factoring, completing the square, or Quadratic Formula. Factorise equation, and look at what x values are needed for the equation to equal zero. Solve the quadratic equation. The x coordinate for all y intercepts is 0, just as the y coordinate for all x intercepts is 0. No, a parabola does not have to have an x-intercept. The y intercept is 0 as well.

The graph of this equation is a parabola as can be easily proved.How many x or y intercepts can a quadratic function have? A x-intercepts and y-intercept B x-intercepts and 1 y-intercept C 2 x-intercepts and 1 y-intercept D x-intercepts and y-intercept I think the answer is D. You only have two choices left First Name.

Your Response. Please Help Guys! The expression has a constant outside of the squared term. The expression is not the product of two binomials. The variable x has a. Determine an expression for the function. Determine the equation of a quadratic function that satisfies each set of conditions. Find the equation for a quadratic function whose vertex is 2,5 and whose graph contains the point -8, I want to learn to learn how to do them.

If a graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or completely solving the related equation?

The graph of a quadratic function can have 0, 1 or 2 x-intercepts. Given the following quadratic equation, find a. Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point.

Write a quadratic function in standard form whose graph passes through. Which description is correct for the x-intercept s of Function A and Function B? Both functions have one negative and one positive x-intercept. Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. You can view more similar questions or ask a new question.

Questions Algebra How many x or y intercepts can a quadratic function have? The variable x has a math the graph of a quadratic function has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Mathematics Determine the equation of a quadratic function that satisfies each set of conditions. Math If a graph of a quadratic function can have 0, 1 or 2 x-intercepts.

College Algrbra Given the following quadratic equation, find a. Write a quadratic function in standard form whose graph passes through Math Which description is correct for the x-intercept s of Function A and Function B?

MATH Create a rational function with a linear binomial in both the numerator and denominator. Label You can view more similar questions or ask a new question. Ask a New Question.The following graphs are two typical parabolas their x-intercepts are marked by red dots, their y-intercepts are marked by a pink dot, and the vertex of each parabola is marked by a green dot:.

We say that the first parabola opens upwards is a U shape and the second parabola opens downwards is an upside down U shape. In order to graph a parabola we need to find its intercepts, vertex, and which way it opens. Notice that the x -intercepts of any graph are points on the x -axis and therefore have y -coordinate 0. If the equation factors we can find the points easily, but we may have to use the quadratic formula in some cases.

If the solutions are imaginary, that means that the parabola has no x -intercepts is strictly above or below the x -axis and never crosses it.

If the solutions are real, but irrational radicals then we need to approximate their values and plot them. The y -intercept of any graph is a point on the y -axis and therefore has x -coordinate 0. We can use this fact to find the y -intercepts by simply plugging 0 for x in the original equation and simplifying. So the y -intercept of any parabola is always at 0,c.

To find the x -coordinate for the vertex we use the following formula:. Since "a" is positive we'll have a parabola that opens upward is U shaped.