https://file.aiquickdraw.com/mathbot/file/1725992960604btwwj9jj.jpg

The quadratic function provided is:

\[
f(x) = -7x^2 - 6x + 10
\]

To find the y-value of the vertex of this quadratic, we can follow these steps:

### 1. Find the x-coordinate of the vertex:
The x-coordinate of the vertex for a quadratic equation \( ax^2 + bx + c \) can be found using the formula:

\[
x = \frac{-b}{2a}
\]

In this case, \( a = -7 \) and \( b = -6 \). Plugging these values into the formula:

\[
x = \frac{-(-6)}{2(-7)} = \frac{6}{-14} = -\frac{3}{7}
\]

### 2. Find the y-value (f(x)) at the vertex:
Now substitute \( x = -\frac{3}{7} \) into the function to find the y-value:

\[
f\left(-\frac{3}{7}\right) = -7\left(-\frac{3}{7}\right)^2 - 6\left(-\frac{3}{7}\right) + 10
\]

Let's compute this step-by-step:

\[
f\left(-\frac{3}{7}\right) = -7\left(\frac{9}{49}\right) + 6\left(\frac{3}{7}\right) + 10 = -\frac{63}{49} + \frac{18}{7} + 10
\]

Simplify further:

\[
f\left(-\frac{3}{7}\right) = -\frac{63}{49} + \frac{126}{49} + \frac{490}{49}
\]

\[
f\left(-\frac{3}{7}\right) = \frac{-63 + 126 + 490}{49} = \frac{553}{49}
\]

Thus, the y-value of the vertex is:

\[
\boxed{\frac{553}{49}} \approx 11.29
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the vertex of a quadratic equation in vertex form?
2. What does the vertex of a parabola represent in real-world contexts?
3. How do you determine whether the vertex is a maximum or minimum?
4. Can the quadratic formula be used to find the vertex?
5. How does changing the coefficient of \( x^2 \) affect the shape of the parabola?

**Tip:** For any quadratic equation, the vertex formula is a quick way to find the turning point of the parabola.

What is the y-value of the vertex of the quadratic function: -7x^2 - 6x + 10?

Learn how to calculate the y-value of the vertex for the quadratic function -7x^2 - 6x + 10. This solution involves using the vertex formula and algebraic substitution, perfect for students in Grades 8-10.

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