7.

Question

Solve x2 – 4 = 5 by graphing the related function.

There is one solution: 1

There are two solutions: ±1.

There are no real number solutions.

There are two solutions: 3 and –3.

Answer 1

To solve the quadratic equation \(x^2 - 4 = 5\) by graphing the related function, follow these steps:

1. **Rewrite the equation**: The given equation \(x^2 - 4 = 5\) can be rewritten as:
\[
x^2 - 4 - 5 = 0
\]
Simplify to get:
\[
x^2 - 9 = 0
\]

2. **Related function**: Let's define the related function:
\[
f(x) = x^2 - 9
\]

3. **Graph the function**: The related function \(f(x) = x^2 - 9\) is a parabola opening upwards with its vertex at \((0, -9)\).

4. **Find the x-intercepts**: To solve for \(x\), set \(f(x) = 0\), which gives:
\[
x^2 - 9 = 0
\]
This simplifies to:
\[
x^2 = 9
\]
Taking the square root of both sides, we get:
\[
x = \pm 3
\]

5. **Interpret the graph**: The graph of \(f(x) = x^2 - 9\) will intersect the x-axis at the points where \(x = 3\) and \(x = -3\).

Therefore, the solutions to the equation \(x^2 - 4 = 5\) are:
\[
\boxed{3 \text{ and } -3}
\]