Mathematics: 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

-2x + 2Step-by-step explanation:...

What is the vertex and the equation of the axis of

jaylasmith884

06.01.2022

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

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