Question

The graph of a quadratic function contains the points

(1,9), (0, 0), and (-1,9). Shawn thinks the function
f(x) = x2 was vertically stretched by a factor of 9. Brielle
thinks the function f(x) = x2 was horizontally shrunk by a
factor of 3. Determine who is correct and explain why.

Answer 1

Both Shawn and Brielle are correct. The absolute value parent function is symmetric with respect to the y-axis, and the absolute value of negative x is a reflection across the y-axis, so the graph of these two functions would look identical. Additionally, if you wanted to verify that the given points are on the graph of both functions, you could substitute them into the functions to get true statements.

Explanation:

Answer on Edge 2021

Answer 2

Shawn is correct.

Explanation:

Let the quadratic function is g(x) = a(x - h)² + k

Here (h, k) is the vertex of the parabola.

Since this parabola passes through (0, 0), (1, 9) and (-1, 9), axis of symmetry is x = 0 and the vertex is (0, 0).

Therefore, equation of the parabola will be,

g(x) = a(x - 0)²+ 0

g(x) = ax²

for a point (1, 9) which lies on the graph,

9 = a(1)²

a = 9

g(x) = 9x² (here a > 1)

Therefore, f(x) is vertically stretched by a factor of 9 to form g(x).

Shawn is correct.