Find a quadratic function of the form 

yequals=ax squaredax2 

that passes through the point 

​(negative 4−4​,negative 32−32​).




To find a quadratic function of the form \( y = ax^2 \) that passes through the point \((-4, -32)\), we can substitute the point's coordinates into the equation and solve for the coefficient \(a\).

Given:
- Point: \((-4, -32)\)
- Function: \(y = ax^2\)

Substitute \(x = -4\) and \(y = -32\) into the equation:

\[
-32 = a(-4)^2
\]

Now, simplify the expression:

\[
-32 = a \cdot 16
\]

Solving for \(a\), we get:

\[
a = \frac{-32}{16} = -2
\]

Therefore, the quadratic function is:

\[
y = -2x^2
\]

### Final Answer:
The quadratic function that passes through the point \((-4, -32)\) is:

\[
\boxed{y = -2x^2}
\]

Would you like to see a graph of this function or further details on quadratic functions?

### Related Questions:
1. How do you find a quadratic function that passes through three points?
2. What are the vertex and axis of symmetry for the quadratic function \(y = -2x^2\)?
3. How does the coefficient \(a\) affect the shape of a quadratic function?
4. What is the process for finding the roots of a quadratic equation like \(y = -2x^2\)?
5. Can you derive the standard form of a quadratic equation from its vertex form?

### Tip:
To identify how a quadratic function behaves, always look at the sign and magnitude of the coefficient \(a\); a negative \(a\) inverts the parabola, while its absolute value determines the "width" or "steepness."

Find a quadratic function of the form y = ax^2 that passes through the point (-4, -32).

Learn how to find a quadratic function of the form y = ax^2 that passes through the point (-4, -32). This example demonstrates solving for the coefficient 'a' and understanding the role of the quadratic equation in algebra. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation