write an equation for f(x) in vertex form. F(x) has a vertex of (-4, 8) and passes through the point (-2,0). 

To write the equation of \( f(x) \) in vertex form, we use the general vertex form of a quadratic equation:

\[
f(x) = a(x - h)^2 + k
\]

Where \( (h, k) \) is the vertex of the parabola.

From the problem, we know the vertex is \( (-4, 8) \), so we can substitute \( h = -4 \) and \( k = 8 \) into the equation:

\[
f(x) = a(x + 4)^2 + 8
\]

Next, we use the point \( (-2, 0) \) to solve for \( a \). Substituting \( x = -2 \) and \( f(x) = 0 \) into the equation:

\[
0 = a(-2 + 4)^2 + 8
\]

Simplify:

\[
0 = a(2)^2 + 8
\]
\[
0 = 4a + 8
\]
\[
4a = -8
\]
\[
a = -2
\]

Now, substitute \( a = -2 \) into the equation:

\[
f(x) = -2(x + 4)^2 + 8
\]

So the equation of \( f(x) \) in vertex form is:

\[
f(x) = -2(x + 4)^2 + 8
\]

Would you like to go over any part of this in more detail?

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Here are 5 related questions you might find useful:
1. How do you identify the vertex of a quadratic equation in vertex form?
2. What is the effect of the value of \( a \) on the graph of the quadratic?
3. How do you convert from vertex form to standard form?
4. How do you determine the axis of symmetry of a parabola given its vertex form equation?
5. What is the significance of the value of \( a \) when the parabola opens upwards or downwards?

**Tip:** Always make sure to double-check that the point you use to solve for \( a \) satisfies the equation once you find \( a \).

Write an equation for f(x) in vertex form. f(x) has a vertex of (-4, 8) and passes through the point (-2, 0).

Learn how to write the equation of a quadratic function in vertex form with a given vertex and point. This step-by-step guide covers the process of using the vertex form formula and solving for the constant 'a' using a specific point on the parabola. Suitable for students in Grades 8-10.

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