Question

What is the vertex and the equation of the axis of symmetry of the graph of y=x2-6x-7?

Answer 1

Answer:

The vertex is (3,-16)  and axis of symmetry is 3

Step-by-step explanation:

The vertex of a quadratic equation $f(x)=ax^{2}+bx+c$ is calculated as $(\frac{-b}{2a},f(\frac{-b}{2a}))$

and the axis of symmetry is  $\frac{-b}{2a}$

Compare equation $y=x^{2}-6x-7$ with $f(x)=ax^{2}+bx+c$

Where a= 1 and b = -6

so, $x=\frac{-b}{2a}=\frac{-(-6)}{2}$

      $x=3$

Now, put the value of x=3 in $y=x^{2}-6x-7$

$y=(3)^{2}-6(3)-7$

$y=9-18-7$

$y=-16$

Therefore, the vertex is (3,-16)  and axis of symmetry is 3

Answer 2

X= -b over 2a = --6 over 2×1=3
y=3²-6(3)-7=-16
vertex is (3,-16)
axis of symmetry is 3