Question

Use the function f(x) to answer the questions:

f(x) = 2x2 − x − 10

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Answer 1

Answer:

x=(-2,0) and x=(5/2,0)

Step-by-step explanation:

To find x-intercepts you set f(x), or y, to 0 and then solve.

$0=2x^2-x-10\\Factor!\\0=(x+2)(2x-5)\\x+2=0\\x=2\\2x-5=0\\2x=5\\x=\frac{5}{2}$

Answer 2

The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).

The function is given as:

$f(x) = 2x^2 - x - 10$

We need to find the points at which the given function crosses the x-axis.

What is the x-intercept of a function?

It is the point at which the given function crosses the x-axis.

The x-intercept is found by setting y = 0 or f(x) = 0.

Given function,

$f(x) = 2x^2 - x - 10$

Let's set f(x) = 0.

$2x^2 - x - 10 = 0$

Solve the equation for x.

$2x^2 - x - 10\\2x^2 - (5 - 4)x - 10\\2x^2 - 5x + 4x - 10\\x(2x-5) +2(2x - 5)\\(x+2)(2x-5)$

Now we have,

x+2 = 0 and 2x - 5 = 0

x = -2 and x = 5 / 2

We already know that y = 0 so the points at which the function intercepts with the x-axis are:

(-2, 0) and (5/2, 0).

The x-intercepts of the graph of f(x) is (-2, 0) and (5/2, 0).

Learn more about x-intercepts of a function here:

https://brainly.com/question/28019177

#SPJ2