To sketch the graphs of f(x) = x2 − 4 and g(x) = -2x - 4:

7.1) To sketch the graphs of $f(x) = x^2 - 4$ and $g(x) = -2x - 4$:

For $f(x) = x^2 - 4$ (parabola):

• Shape: Opens upwards.
• y-intercept: Set $x=0 \implies f(0) = 0^2 - 4 = -4$. Point: $(0, -4)$.
• x-intercepts: Set $f(x)=0 \implies x^2 - 4 = 0 \implies (x-2)(x+2) = 0 \implies x = 2$ or $x = -2$. Points: $(2, 0)$ and $(-2, 0)$.
• Turning point: For $f(x) = ax^2 + bx + c$, the x-coordinate of the turning point is $x = \frac{-b}{2a}$. Here, $a=1, b=0$, so $x = \frac{0}{2(1)} = 0$. The y-coordinate is $f(0) = -4$. Point: $(0, -4)$.

For $g(x) = -2x - 4$ (straight line):

• y-intercept: Set $x=0 \implies g(0) = -2(0) - 4 = -4$. Point: $(0, -4)$.
• x-intercept: Set $g(x)=0 \implies -2x - 4 = 0 \implies -2x = 4 \implies x = -2$. Point: $(-2, 0)$.

Sketching instructions:
Draw a Cartesian plane with x and y axes.

1. Plot the points $(0, -4)$, $(2, 0)$, and $(-2, 0)$ for $f(x)$. Draw a smooth parabola passing through these points, opening upwards, with $(0, -4)$ as its minimum turning point.
2. Plot the points $(0, -4)$ and $(-2, 0)$ for $g(x)$. Draw a straight line passing through these two points. Notice that both graphs intersect at $(0, -4)$ and $(-2, 0)$.

7.2) Use your graphs to determine the values of x if:

7.2.1) $f(x) = g(x)$
This occurs at the intersection points of the two graphs.