Question

What is the vertex and the equation of the axis of symmetry of the graph of y=x^2-6x-7

A. vertex: (–16, 3)
a.o.s: x = –16

B. vertex: (–3, 20)
a.o.s: x = –3

C. vertex: (3,–16)
a.o.s: x = 3

D. vertex: (20, –3)
a.o.s: x = 20

Answer 1

Using the formula x = -b/(2a) We get x = 6/2=3 There is only one choice with x =3 so c is the answer

Answer 2

Answer:

Option C is correct

Vertex: (3, -16) and axis of symmetry is x = 3

Step-by-step explanation:

The axis of symmetry for a parabolic general equation $y=ax^2+bx+c$ is given by:

$x = -\frac{b}{2a}$            ....[1]

Vertex of the equation is: $(-\frac{b}{2a}, f(-\frac{b}{2a})$

As per the statement:

The graph of the equation is:

$y=f(x) = x^2-6x-7$          ....[2]

On comparing with general parabolic equation i.e  $y=ax^2+bx+c$ we have;

a = 1, b = -6 and c = -7

By [1] we have;

$x = -\frac{b}{2a}$

Substitute the given values we have;

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

Simplify:

x = 3

Substitute the value  of x= 3 in [2] we have;

$f(3) = 3^2-6(3)-7=9-18-7=-9-7=-16$

Therefore, the vertex of the given equation is: (3, -16) and axis of symmetry is x = 3