Question

The equation for a parabola stretched by a factor of 4 opening downward and shifted 12 units down and 3 units to the left

Answer 1

We have been given a parabola with certain characteristics and we need to write down the equation of the parabola.

The general form of a parabola is given by:

`y\pm k=\pm a(x\pm h)^2`

Each of the constants, k, a, and h all correspond to certain characteristics which will help us solve the problem.

k:

This is what we use to shift the parabola up or down the y-axis. When k is positive, the graph shifts downwards and if k is negative, the graph is shifted upwards

h:

This is what we use to shift the parabola right or left about the x-axis. When h is positive, the graph is shifted to the left and if h is negative, the graph is shifted to the right

a:

This is what determines how wide (stretched) or how narrow (compressed) the parabola will be. If a is positive, then the parabola will open upwards and if a is negative, the parabola will open downwards. Also, if a is between 0 and 1, the parabola becomes stretched while if the value of a is greater than 1, the parabola compresses

Hence, with the following information, we can solve the question.

k = +12

a = -1/4

h = 3

Therefore, we can write the equation as:

`y+12=-(1)/(4)(x+3)^2\text{ (THIS IS THE FINAL ANSWER)}`

For further confirmation, the parent function and the shifted graph (like the question demands

are shown below)

PARENT GRAPHT

This graph is unshifted and still narrow.

SHIFTED GRAPH

Once again, the final answer is:

`y+12=-(1)/(4)(x+3)^2`