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:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
For the equation \( 4x^2 + 9x - 9 = 0 \), the coefficients are:
- \( a = 4 \)
- \( b = 9 \)
- \( c = -9 \)
Now, we can calculate the discriminant \( b^2 - 4ac \):
\[ b^2 - 4ac = 9^2 - 4(4)(-9) = 81 + 144 = 225 \]
Next, we substitute the values into the quadratic formula:
\[ x = \frac{-9 \pm \sqrt{225}}{2 \cdot 4} \] \[ x = \frac{-9 \pm 15}{8} \]
Now we calculate both possibilities:
- Using \( +15 \):
\[ x = \frac{-9 + 15}{8} = \frac{6}{8} = \frac{3}{4} \]
- Using \( -15 \):
\[ x = \frac{-9 - 15}{8} = \frac{-24}{8} = -3 \]
Thus, the zeros of the graph are \( x = \frac{3}{4} \) and \( x = -3 \).
Given the options you provided, it seems like they do not contain the correct answers. However, the correct zeros are \( \frac{3}{4} \) and \( -3 \).