Equation for a function that has a graph with the given characteristics

Question

the shape of y=x^2, shifted right 3 units, vertically stretched by 4, and down 7 units

Answer 1

You'll want to check out the vertex form of the quadratic equation:

y = a(x – h)² + k

The vertex of the equation is (h, k), and a is a multiplying factor (which is what I'll assume the "vertically stretched" part of your question refers to.

If your function is shifted to the right 3 units, that means that the x-value of the vertex would shift to the right (positive) by that amount; therefore:

h = 3

It's also shifted down 7 units, which means that the y-value of the vertex would shift down (negative) by that amount; therefore:

k = -7

And if it's "vertically stretched" by 4, that would change our a value:

a = 4

Finally, plugging it into our vertex form of the quadratic equation, we get:

y = 4(x – 3)² – 7