Question

The graphs of $f$ and $g$ are shown. Describe two different transformations from the graph of $f$ to the graph of $g$ . 2 lines labelled f and g are plotted on a coordinate plane. The first labeled f line passes through the points, ordered pair negative 1 comma negative 3, ordered pair 0 comma negative 1 and ordered pair 2 comma 3. The second line labeled g passes through the points, ordered pair negative 3 comma negative 3, ordered pair negative 1 comma 1 and ordered pair 0 comma 3.

Answer 1

Let's convert the word descriptions into mathematical equations first for illustration.

f(x) = x^2 - x - 12

g(x) = -2.5x - 2

Then, we equate g(x) and f(x). The final equation becomes

x^2 - x - 12 = -2.5x - 2

Then, we simplify by transposing and combining like terms.

x^2 - x + 2.5x -12 + 2 = 0

x^2 + 1.5x - 10 = 0

Since this is a quadratic equation, we find the roots by using the quadratic formula

where a = 1, b = 1.5 and c=-10

Thus, the answer is x = 2.5, -4.