Question

1. using your calculator, graph the following functions and find the solution to the system.

\\(f(x) = x^2 + x - 4\\)
\\(g(x) = -2x^2 - 2x + 14\\)

(4, 14)
(-3, 2) and (2, 2)
no solution, they do not intersect.
(-2.5, 5) and (1.5, 5)

Explanation:

Set up the system of equations

To find the intersection points of the two functions, we set \(f(x) = g(x)\).

$$ x^2 + x - 4 = -2x^2 - 2x + 14 $$

Rearrange into standard quadratic form

Using the Algebraic Simplification knowledge point

$$
LATEXBLOCK0
$$

Divide by the common factor

Using the Algebraic Simplification knowledge point

$$
LATEXBLOCK1
$$

Solve the quadratic equation

Using the Factoring Trinomials and Zero Product Property knowledge points

$$
LATEXBLOCK2
$$

Find the corresponding y-coordinates

Using the Algebraic Evaluation knowledge point

$$
LATEXBLOCK3
$$

The intersection points are \((-3, 2)\) and \((2, 2)\).

Answer:

• (A) \((-4, 14)\)
• (B) \((-3, 2)\) and \((2, 2)\) (Correct answer)
• (C) No solution, they do not intersect.
• (D) \((-2.5, 5)\) and \((1.5, 5)\)