Question

Find the axis of symmetry, vertex, domain, range to y=x^2-6x=+7

Answer 1

First, we want to get the +7 on the other side of the equal sign, so we subtract 7 on both sides.

x^2 - 6x - 7 = 7 - 7
x^2 - 6x - 7

Next, we use the formula $\frac{-b}{2a}$ to find the axis of symmetry.
Because this is a quadratic equation, it is in the form
ax^2 + bx + c
We need to identify the a b and c values.

ax^2 + bx + c
(1)x^2 - 6x - 7
a = 1, b = -6 and c = -7.

Substitute the a and b values into the equation to find the axis of symmetry.

$\frac{-b}{2a}$ = $\frac{-(-6)}{2(1)}$ = $\frac{6}{2}$ = 3

The axis of symmetry is is 3.
The axis of symmetry is also the x coordinate of our vertex.
To find the y coordinate, substitute the axis of symmetry we found into the original quadratic equation by replacing each x variable with 3.

x^2 - 6x - 7
(3)^2 - 6(3) - 7
9 - 18 - 7
-16

The vertex is (3, -16)

The domain represents all possible x-values of the parabola. Because our function will always be getting wider graphically, it will cover every possible x value. The domain is all real numbers.

The range represents all possibly y values. The parabola will always be going up, but it only goes as far down as to the minimum vertex, making the range all real numbers that are greater than or equal to −16. The range can be written as y ≥ −16.

So,

Axis of symmetry: 3
Vertex: (3, -16)
Domain: All real numbers
Range: y ≥ −16

Hope this helps!!
Let me know if there's anything you don't understand and I'll try to explain as best I can.