To find the equation of the parabola in intercept form, we'll use the formula for a quadratic function in intercept form:

$y = a(x - p)(x - q)$

Where $p$ and $q$ are the x-intercepts, and $a$ is a constant to be determined.

Step 1: Identify the known values

• The x-intercepts are given as $p = -7$ and $q = -3$.
• The parabola also passes through the point $(-2, 0.05)$, which we will use to find the value of $a$.

Step 2: Set up the equation

Using the x-intercepts $p = -7$ and $q = -3$, the equation becomes:

$y = a(x + 7)(x + 3)$

Step 3: Solve for $a$

We substitute the point $(-2, 0.05)$ into the equation to find $a$:

$0.05 = a(-2 + 7)(-2 + 3)$

Simplifying the terms inside the parentheses:

$0.05 = a(5)(1)$

This simplifies to:

$0.05 = 5a$

Solving for $a$:

$a = \frac{0.05}{5} = 0.01$

Step 4: Write the final equation

Now that we know $a = 0.01$, the equation of the parabola is:

$y = 0.01(x + 7)(x + 3)$

This is the equation of the parabola in intercept form.

Would you like further details or have any questions?

Here are five related questions you might explore:

1. How do you convert intercept form into standard form?
2. What would happen to the parabola if the value of $a$ were negative?
3. How do you find the vertex of the parabola given in intercept form?
4. Can you find the axis of symmetry for this parabola?
5. How do changes in the x-intercepts affect the width of the parabola?

Tip: The value of $a$ determines whether the parabola opens upward ($a > 0$) or downward ($a < 0$), as well as its width.