Question

Describe the changes that occur to the quadratic function (based on the parent function). Check ALL that apply.

4 = (x - 3)^2 + 5
a) Shrink by a factor of 4
b) Stretch by a factor of 4
c) Left by 3
d) Right by 3
e) Down by 5
f) Up by 5

Answer 1

The quadratic function 4 = (x - 3)^2 + 5 shows that the parabola is shifted right by 3 units and up by 5 units from the parent function. There is no vertical stretch or shrink indicated in this function.

Step-by-step explanation:

To describe the changes that occur to the quadratic function based on the parent function for the equation 4 = (x - 3)^2 + 5, we need to compare this equation to the standard form of a quadratic function, which is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola and 'a' determines the width of the parabola.

In this case, 'a' is not explicitly given, so it is assumed to be 1 (since there is no coefficient multiplying the (x - 3)^2 term), meaning there is no vertical stretch or shrink. The equation can be rewritten as f(x) = (x - 3)^2 + 5, indicating that the parabola is shifted to the right by 3 units (h = 3) and up by 5 units (k = 5). Therefore, 'c' and 'f' are the correct choices describing the transformations.