Question

The answer for:

Consider the quadratic equation x^2 - 6x - 16 = 0.
A. Solve the equation, and discuss how the type of roots affects the appearance of the graph of the function y = x^2 - 6x - 16.
B. What is the vertex of the graph of x^2 - 6x - 16 = 0?
C. What is the equation of the axis of symmetry?
D. Use this information to draw a rough sketch of the graph of the function.

Answer 1

A. Solution=(x-8)(x+2),Zeros are 8,-2

The integer coefficient of x² is >1 and so the graph which is a parabola,curves downward and opens upward

B. The vertex or turning point is the minimum point =-b/2a=-(-6)/2(1)=3

f(3)=(3)²-6(3)-16=-25

the vertex occurs at y=-25

C. Equation of the axis of symmetry =-b/2a

which is x=3