Question

Part 1: Predict the change from the parent function f(x)=x2 for each function. (Explain how it willlook different or transformed)1) g(x) = 4x22) h(x) = 5x23) j(x) = -3x2

Answer 1

See explanation below

Explanation:

Parent function = x²

For a parabola: y = ax²

If a approached a number greater than zero, the parabola becomes narrow. As a approaches, 0, the parabola widens.

1) g(x) = 4x²

Initial value of a in the parent function = 1

The value of a in this function = 4

4 > 1

This means the parabola will become narrow. And the parent function will be wider

2) h(x) = 5x²

a = 5

Initial value of a in the parent function = 1

5 > 1

The parabola will be more narrow than that of 4x².

3) j(x) = -3x²

a = -3

In this case, a is less than zero.

When a is greater than zero, the parabola opens upward. When it is less than zero, it opens downward.

From the graph, we will see the parabola opens downward.

The vertex in each of the graph remains the same.