Question

Write the equation of the following graph in vertex form.

1) f(x) -0.4 (x + 2)(x - 5)
2) f(x) 0.4 (x + 2)(x - 5)
3) f(x) -0.4 (x - 2)(x + 5)
4) f(x) 0.4 (x - 2)(x + 5)

Answer 1

The quadratic equation in vertex form is f(x) = 0.4(x - 2)² + 5

How to determine the equation in vertex form

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have the vertex to be

(h, k) = (2, 5)

A quadratic equation in vertex form is represented as

f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 2)² + 5

Using the points, we have

a = 0.4

Substitute the known values into the equation

f(x) = 0.4(x - 2)² + 5

Hence, the equation in vertex form is f(x) = 0.4(x - 2)² + 5

Answer 2

Correct choice is 2.
`f(x)=0.4(x+2)(x-5)`

Explanation:

We have been given a graph of the quadratic function. Now we need to use that graph to find the equation of the graph in vertex form. By the way given choices written in intercept form so to be accurate we are going to find the equation in intercept form.

from graph we see that x-intercepts are at 5 and -2.

we know that if x=a is x-intercept then (x-a) must be factor.

So (x+2)(x-5) is the factor.

when leading coefficient is positive then graph opens upward.

so that means leading coefficient is 0.4

Hence correct choice is 2.
`f(x)=0.4(x+2)(x-5)`