Question

What are the zeros of the graph of: y = 4x^2 + 9x - 9

Answer 1

To find the zeros of the quadratic function \( y = 4x^2 + 9x - 9 \), we need to solve the equation:

\[
4x^2 + 9x - 9 = 0
\]

We can use the quadratic formula, which is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this case, the coefficients are:
- \( a = 4 \)
- \( b = 9 \)
- \( c = -9 \)

First, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 9^2 - 4(4)(-9) = 81 + 144 = 225
\]

Since the discriminant is positive, there will be two real and distinct solutions. Next, we apply the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{225}}{2 \cdot 4}
\]

Calculating \( \sqrt{225} \):

\[
\sqrt{225} = 15
\]

Now substituting back into the formula:

\[
x = \frac{-9 \pm 15}{8}
\]

This gives us two possible solutions:

1. \( x = \frac{-9 + 15}{8} = \frac{6}{8} = \frac{3}{4} \)

2. \( x = \frac{-9 - 15}{8} = \frac{-24}{8} = -3 \)

Thus, the zeros of the graph of the function \( y = 4x^2 + 9x - 9 \) are:

\[
x = \frac{3}{4} \quad \text{and} \quad x = -3
\]