Question

PLEASE HELP ASAPPP!!!!

The function f(x) is shown on the graph.

The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.

What is the standard form of the equation of f(x)?

f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7

Answer 1

f(x)= -x^2-6x+7

Explanation:

Since the graph opens downward the function for the parabola is going to be negative. This leaves us with two answers.

Now use the remaining possible equations and solve for the vertex.

Using x= -b/2a to solve for the x value of the vertex plug in the values to solve.

a= -1 b= -6 c=7 so, since -6 is already negative plugging it in makes it positive -(-6)/2(-1) = 6/-2 = -3. So x equals negative 3.

Then plug in -3 into the equation to get the y-value.

- (-3)^2 - 6(-3) + 7 = -9 + 18 + 7 = 16 so this confirms the vertex for this equation is (-3,16) so the answer is -x^2-6x+7.

Hope this helped! :)