Question

For the graph of each function, find an equation of the line of symmetry and the coordinates of the vertex. Tell whether the value of the function at the vertex if a maximum or a minimum:

a) y = -x^2 + 4x - 7;


b) y = 2x^2 + 4x;


c) y = -3x^2 - 18x + 5.

Answer 1

For all these problems, we only have to complete the squares and transform the equations to the form
y=a(x-h)²+k
then (h,k) is the vertex.
If a>0, the vertex is a minimum, and
if a<0, then the vertex is a maximum.

a)
y=-x²+4x-7
=-1(x-2)²-3
So (h,k)=(2,-3) is the vertex.
Since a=-1, the vertex is a maximum.

I will leave (b) and (c) for you as exercises as they were intended.