I need help plzz

Question

A quadratic function is defined by . Does the vertex represent the minimum value of the maximum vlaue of the function? Explain or show how you know.

Answer 1

general form of the quadratic equation with a vertical parabola is

y = a(x-h)^2 + k where the vertex is (h,k) which is the minimum point if a>0

the vertex is the maximum point if a<0

In the given problem there is an implicit +1 = a, so the vertex (-4,7) is the minimum point

It's an upward opening parabola

IF you had a standard quadratic equation with vertex at the origin, it would be y=x^2. the implicit +1 for the coefficient of the x^2 term means the vertex (the origin) is the minimum point. (0,0) has y=0 since x^2 is always positive, 0 is the minimum y value