Question

A quadratic equation g(x), has x-intercepts 5 and -1. In addition, (2,-9) satisfies f(x). Two transformations are applied to g(x). First, it is reflected over the x-axis and then it is stretched vertically by a factor of 3.Find the y-intercept of g(x)

Answer 1

(0,15)

1) Since the g(x) function has x-intercepts "5" and "-1" then we can write the quadratic factored form:

$\begin{gathered} y=a(x-x_1)(x-x_2) \\ y=a(x-5)(x+1) \end{gathered}$

2) Since we were told that this g(x) function has been reflected over the x-axis and stretched vertically by a factor of 3, we can rewrite that "a" coefficient that way:

$g(x)=-3(x-5)(x+1)$

3) So, let's expand that to get the function and the y-intercept:

$\begin{gathered} g(x)=-3(x-5)(x+1) \\ g(x)=-3(x^2+x-5x-5) \\ g(x)=-3x^2+12x+15 \\ \\ \end{gathered}$

Note that the minus sign in the leading coefficient points out that the equation has been vertically stretched and reflected in comparison to the parent function.

Thus, the y-intercept of g(x) is (0,15)