Write an equation for the quadratic graphed below
x
 -intercepts: (-2,0) and (1,0).  
y
 -intercept: (0,3)


1
2
3
4
5
-1
-2
-3
-4
-5
1
2
3
4
5
-1
-2
-3
-4
-5
 

y
  = 

Given the information about the x-intercepts \((-2,0)\) and \((1,0)\) and the y-intercept \((0,3)\), we can construct the quadratic equation in the factored form as follows:

The general form of a quadratic equation with known x-intercepts is:

\[
y = a(x - x_1)(x - x_2)
\]

where \(x_1\) and \(x_2\) are the x-intercepts.

For the x-intercepts \((-2,0)\) and \((1,0)\), the equation becomes:

\[
y = a(x + 2)(x - 1)
\]

Now, use the y-intercept \((0,3)\) to find the value of \(a\). Substituting \(x = 0\) and \(y = 3\) into the equation:

\[
3 = a(0 + 2)(0 - 1)
\]

\[
3 = a(2)(-1)
\]

\[
3 = -2a
\]

Solving for \(a\):

\[
a = -\frac{3}{2}
\]

Thus, the equation of the quadratic is:

\[
y = -\frac{3}{2}(x + 2)(x - 1)
\]

Expanding this equation:

\[
y = -\frac{3}{2}(x^2 + x - 2)
\]

\[
y = -\frac{3}{2}x^2 - \frac{3}{2}x + 3
\]

So, the quadratic equation is:

\[
y = -\frac{3}{2}x^2 - \frac{3}{2}x + 3
\]

Would you like further details or clarification on any steps?

Here are 5 related questions:
1. How do you factor a quadratic equation from a graph?
2. What is the significance of the y-intercept in a quadratic equation?
3. Can you solve the quadratic equation using the quadratic formula instead?
4. How do you determine the vertex of a quadratic equation from its graph?
5. What role does the coefficient \(a\) play in the shape of the parabola?

**Tip**: The sign of \(a\) in a quadratic equation determines if the parabola opens upward or downward!

Write an equation for the quadratic graphed below: x-intercepts (-2,0) and (1,0), y-intercept (0,3).

Discover how to construct the quadratic equation for a parabola with x-intercepts at (-2,0) and (1,0) and a y-intercept at (0,3). This step-by-step solution covers algebraic methods for factoring and solving quadratics, suitable for students in Grades 9-10.

Math Problem Statement

y

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation