Question

An expression is shown below: f(x) = 2x2 − x − 10 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points) (10 points)

Answer 1

Explanation:

X intercepts are when y = 0 also, and remember this, when there is an intercept , that's also called a "root" . It's a really common question for a test to say .... "find the roots" and then you are wondering what the heck do they want. :P

A)

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

when does f(x) = 0 ?

2
`x^(2)` - x - 10 = 0

2(
`x^(2)` -
`(1)/(2)`x - 5) = 0

factor it

(x-2.5)(x+2)

we know when x= 2.5 and when x = -2 we have zeros or roots

B)

find the derivative of f(x)

4x-1

when does 4x-1 = 0

at
`(1)/(4)`

now plug
`(1)/(4)` into our original equation, to find the y coordinate

-10.125

vertex at (
`(1)/(4)` , -10.125 )

C)

graph it by using the vertex, and the roots to find those points. i'm attaching a graph