Question

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

Answer 1

Answer:

A

Step-by-step 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:

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

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

Find the x-coordinate of the vertex:

$\displaystyle x = -\frac{(-6)}{2(1)} = 3$

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.