Answer:
Correct choice is A
Step-by-step explanation:
Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
The x-intercepts are the points where the graph of the function crosses the x-axis, they are also called zeros or roots. They can be found by solving the equation y=0,
The y-intercepts are the points where the graph of the function crosses the y-axis. They can be found by setting x=0.
We are given the function:
[tex]y = f(x)=x^2+6x-16[/tex]
Find the y-intercept. x=0:
[tex]f(0)=0^2+6*0-16=-16[/tex]
y-intercept: (0,-16)
Find the x-intercepts, y=0. Solve the equation
[tex]x^2+6x-16=0[/tex]
Factoring:
[tex](x-2)(x+8)=0[/tex]
Which gives x=2, x=-8.
X-intercepts (2,0) (-8,0)
This leaves us only choice A as correct. But we'll compute the vertex also.
Completing squares:
[tex]y=x^2+6x-16=x^2+6x+9-16-9=(x+3)^2-25[/tex]
Comparing with the vertex form of the function, we have: h=-3, k=-25, thus the vertex is located at (-3,-25)
This confirms that the correct choice is A
