Please Solve It ..... :)

Question

The Graph of a Quadratic Function contains (4, -64) and its vertex is at the Origin.

a. Write an Equation for this Function.

b. Does the Equation show a Streatch or a Shrink of its parent equation.

Answer 1

y = ax^2

-64 = a(4^2 = 16a

a =-64/16 = -4

y or f(x) = -4x^2

if the parent equation is y=x^2

y=-4x^2 is narrower and that's a stretch

if a>1 or a<-1 it's a stretch

if -1<a<1, it's a shrink or compression

(don't tell psychiatrists this. They don't like being called "shrinks" that would be a stretch of vocabulary meaning, so to speak. Think of "stretch" as like what Spain's Inquisitor Torquemada did to suspected heretics and witches: put them on a rack and stretch their bodies until they confessed. Good way to grow an inch or two, but it could pull a few joints out of their sockets. Not recommended. Still the idea is you get narrower, like the parabola that's stretched)

Answer 2

a.

The parent function of a parabola with a vertex at (h,k) and an amplitude is written so, y - k = a (x - k)².

The parent function of a parabola with a vertex at the origin can be written as y = ax².

The parabola passes through (x,y) = (4,-64).

Using the formula, that gives:

y = ax²

-64 = a (4)²

-64 = a (16)

-64/16 = a

-4 = a

Filling in the unknown, a, the formula gives:

y = a (x)²

y = -4 (x)²

y = -4x²

b.

The parabola is open downward (since a = negative) and shows a stretch (since |-4| is greater than 1).