Y=½(x+2)² parabola

Question

What is the direction of opening, vertex, equation of the axis of symmetry, max\min value and stretch/compression/reflection of the following parabolas...

Y=½(x+2)²

Y=4x²-5

Y=-(x+1)²-2

Pleeaaassee help, due tm

Answer 1

The vertex form of Quadratic equation is:

 

y = a(x-h)² + k  where (h,k) is the vertex (which is also the min or max) and a is the dilation/reflection factor

 

For the first problem, the vertex is (-2,0), it opens up (because a is positive), it is compressed by a factor of 1/2, the vertex is the minimum and the max is +inf, the axis is symmetry is x=-2.

 

For the second, vertex is (0,-5), opens up, stretched by a factor of 4, the vertex is the min, max is +inf and x=0 is the axis of symmetry

 

For the 3rd, the vertex is (-1, -2), opens down, no stretch/compression factor, the vertex is tghe max and min is -inf, axis of symmetry is x=-1