i was trying to understand some math questions but im not getting them?

Question

give an equation that matches each description:

A parabola that is upside down and default size

A parabola that is facing up and wider

Describe the graph of y=-4x^2 +3

Answer 1

a) y = -x^2

b) y = (1/2) x^2

c) A narrow downward-facing parabola which peaks at (0,3) and intercepts the x-axis at +/- sqrt(3)/2

Answer 2

A parabola that is upside down and default size:
y = - x^2
(The negative sign "flips" the parabola over the x-axis.)

A parabola that is facing up and wider:
y = (1/2)x^2
(Put any positive constant less than one in front of the x^2, and you will get a "wider" parabola facing up. I chose (1/2), but you could pick a different postive constant less than one.)

Describe the graph of y=-4x^2 +3:
This is a prabola that is facing down. It has been shifted up three units so the vertex is at the point (0, 3) rather than at the origin. It is also more narrow than the "default size" since the constant in front of the x has an absolute value greater than one.

Answer 3

y=-4x^2 +3

this is a parabola because it is linear in y and to a positive power of x.

it opens downward because the x^2 term is negative

it is symetrical about the y axis because their is no linear term of x

the vertex is at y equal 3 because this is the single value obtained when x = 0.