Question

Which of the following graphs is described by the function given below?
y = x2 - 6x-7 ​

Answer 1

A

Explanation:

We are given the function:

`\displaystyle y = x^2 - 6x - 7`

And we want to determine its graph.

One of the most important features of a quadratic is its vertex. So, we can start by finding the vertex using the formulas:

`\displaystyle \text{Vertex} = \left(-(b)/(2a), f\left(-(b)/(2a)\right)\right)`

In this case, a = 1, b = -6, and c = -7.

Find the x-coordinate of the vertex:

`\displaystyle x = -((-6))/(2(1)) = 3`

Substitute this back into the equation to find the y-coordinate:

`\displaystyle y(3) = -16`

Therefore, our vertex is at (3, -16).

The only graph whose quadratic's vertex is at (3, -16) is Graph A. Thus, our answer is A.