Write the equation of the parabola that has its vertex at and
passes through the point in form.
The equation of the parabola in form is .

Ask by Gray Salazar. in the United States

Dec 18,2024

Question

Write the equation of the parabola that has its vertex at and
passes through the point in form.
The equation of the parabola in form is .

Ask by Gray Salazar. in the United States

Dec 18,2024

UpStudy AI · Accepted Answer

To find the equation of the parabola in the form $$ f(x) = a(x - h)^2 + k $$, we start with the vertex form of the parabola, where $$ (h, k) $$ is the vertex. Given that the vertex is at $$ (-5, -1) $$, we have:

$$
h = -5 \quad \text{and} \quad k = -1
$$

Thus, the equation becomes:

$$
f(x) = a(x + 5)^2 - 1
$$

Next, we need to determine the value of $$ a $$. We know that the parabola passes through the point $$ (-4, -8) $$. We can substitute $$ x = -4 $$ and $$ f(x) = -8 $$ into the equation to find $$ a $$:

$$
-8 = a(-4 + 5)^2 - 1
$$

This simplifies to:

$$
-8 = a(1)^2 - 1
$$

$$
-8 = a - 1
$$

Now, we solve for $$ a $$:

$$
a = -8 + 1
$$
$$
a = -7
$$

Now that we have $$ a $$, we can write the complete equation of the parabola:

$$
f(x) = -7(x + 5)^2 - 1
$$

Thus, the equation of the parabola in $$ f(x) = a(x - h)^2 + k $$ form is:

$$
\boxed{f(x) = -7(x + 5)^2 - 1}
$$
f(x) = -7(x + 5)^2 - 1

Write the equation of the parabola that has its vertex at and
passes through the point in form.
The equation of the parabola in form is .

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Write the equation of the parabola that has its vertex at and passes through the point in form. The equation of the parabola in form is .

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Write the equation of the parabola that has its vertex at and
passes through the point in form.
The equation of the parabola in form is .