# Quadratic functions: Which of these quadratic functions has exactly one x -intercept

• MHB
• yormmanz
In summary: Re: help quadricHello again! It looks like your answers for the first two questions were correct. For the third question, the correct answer is actually (A) y=4x^2-2x-1. Remember that a parabola opens upward when the leading coefficient is positive and appears narrower when the leading coefficient is larger. So (A) has a larger leading coefficient than (C), making it the correct choice. Keep up the good work!
yormmanz
5. Which of these quadratic functions has exactly one x -intercept?
o A. y=x 2 −9
o B. y=x 2 −6x+9
o C. y=x 2 −5x+6
o D. y=x 2 +x−6

A

2. What are the x-intercepts of y=(x−2)(x+5) ?
o A. (0, 2) and (0, -5)
o B. (0, -2) and (0, 5)
o C. (-2, 0) and (5, 0)
o D. (2, 0) and (-5, 0)

D

5. Which of these quadratic functions has exactly one x -intercept?
o A. y=x 2 −9
o B. y=x 2 −6x+9
o C. y=x 2 −5x+6
o D. y=x 2 +x−6

A

2. Which of the following parabolas opens upward and appears narrower than y=−3x 2 +2x−1 ?

o A. y=4x 2 −2x−1
o B. y=−4x 2 +2x−1
o C. y=x 2 +4x
o D. y=−2x 2 +x+3

thanks

Guest

Hello, and welcome to MHB! (Wave)

Let's look at the first one...when a quadratic function has one real root, then its discriminant will be zero, or equivalently, it can be written in the form:

$$\displaystyle f(x)=(x-r)^2$$ where $$r\in\mathbb{R}$$

We see that choice A has a discriminant of $$0^2-4(1)(-9)=36$$. Can you proceed to find the correct choice?

yormmanz said:
5. Which of these quadratic functions has exactly one x -intercept?
o A. y=x 2 −9
o B. y=x 2 −6x+9
o C. y=x 2 −5x+6
o D. y=x 2 +x−6
Just a quick FYI: The first equation may be written as y = x^2 - 9. It seems obvious but not including the ^ can potentially cause confusion.

-Dan

yormmanz said:
5. Which of these quadratic functions has exactly one x -intercept?
o A. y=x 2 −9= (x- 3)(x+ 3)
o B. y=x 2 −6x+9= (x- 3)^2
o C. y=x 2 −5x+6= (x- 3)(x- 2)
o D. y=x 2 +x−6= (x+ 3)(x- 2)

A
The x-axis has y= 0 for all points so an "x- intercept" is where y= 0. Set each of those formulas equal to 0 and solve for x. A quadratic equation may have one (double) root, two real roots, or no real root. Which of those equations has exactly one (double) root.
2. What are the x-intercepts of y=(x−2)(x+5) ?
o A. (0, 2) and (0, -5)
o B. (0, -2) and (0, 5)
o C. (-2, 0) and (5, 0)
o D. (2, 0) and (-5, 0)

D

Again, the x-intercepts are where y= 0. That immediately removes (A) and (B) as possible answers. What are the roots of (x- 2)(x+ 5)= 0?

5. Which of these quadratic functions has exactly one x -intercept?
o A. y=x 2 −9= (x- 3)(x+ 3)
o B. y=x 2 −6x+9= (x- 3)^2
o C. y=x 2 −5x+6= (x- 3)(x- 2)
o D. y=x 2 +x−6= (x+ 3)(x- 2)

A
Set each equal to 0 and solve the equations for x! Which has a double root?

2. Which of the following parabolas opens upward and appears narrower than y=−3x 2 +2x−1 ?

o A. y=4x 2 −2x−1
o B. y=−4x 2 +2x−1
o C. y=x 2 +4x
o D. y=−2x 2 +x+3

C
A parabola opens upward if and only if the leading coefficient (the coefficient of x^2) is positive. Further the larger that leading coefficient is the "narrower" the parabola is. The correct answer is "A", not "C".

Are my answers correct or not

thanks

Guest

Last edited:

## 1. What is a quadratic function?

A quadratic function is a polynomial function with the highest degree of 2, represented by the general form f(x) = ax^2 + bx + c. It is a type of function that creates a parabolic curve when graphed.

## 2. What is an x-intercept?

An x-intercept is a point on the graph of a function where the curve intersects the x-axis. It is also known as the root or solution of the function, where the value of y is equal to 0.

## 3. How can you determine the number of x-intercepts a quadratic function has?

A quadratic function can have 0, 1, or 2 x-intercepts, depending on the value of the discriminant (b^2 - 4ac). If the discriminant is positive, the function will have 2 x-intercepts. If it is 0, the function will have 1 x-intercept. And if it is negative, the function will have 0 x-intercepts.

## 4. What is the significance of a quadratic function having exactly one x-intercept?

A quadratic function with 1 x-intercept means that the parabola intersects the x-axis at only one point. This also means that the function has only one real root or solution, which can be useful in solving real-life problems.

## 5. How can you identify a quadratic function that has exactly one x-intercept?

A quadratic function that has exactly one x-intercept will have a discriminant of 0, meaning that the expression b^2 - 4ac will equal 0. This can also be seen in the graph of the function, where the parabola touches the x-axis at only one point.

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