Question

1. determine the values of x for which the function f(x) = -3(x + 4)^2 + 5 is equal to -7. 12. find the rule of the quadratic function represented by a parabola with a vertex at v(-5) and

Explanation:

Step1: Set function equal to -7

$$-3(x + 4)^2 + 5 = -7$$

Step2: Isolate the squared term

Subtract 5 from both sides:
$$-3(x + 4)^2 = -7 - 5$$
$$-3(x + 4)^2 = -12$$
Divide both sides by -3:
$$(x + 4)^2 = 4$$

Step3: Solve for x

Take square root of both sides:
$$x + 4 = \pm 2$$
Solve for each case:
Case 1: $x + 4 = 2$ → $x = 2 - 4 = -2$
Case 2: $x + 4 = -2$ → $x = -2 - 4 = -6$

Answer:

$x = -6$ and $x = -2$