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:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 4 \), \( b = 9 \), and \( c = -9 \).
First, we calculate the discriminant:
\[ b^2 - 4ac = 9^2 - 4(4)(-9) = 81 + 144 = 225 \]
Now we can find the roots using the quadratic formula:
\[ x = \frac{-9 \pm \sqrt{225}}{2 \cdot 4} \]
Calculating the square root and the denominator:
\[ \sqrt{225} = 15 \]
So we have:
\[ x = \frac{-9 \pm 15}{8} \]
Now, we will calculate the two possible values for \( x \):
-
\( x = \frac{-9 + 15}{8} = \frac{6}{8} = \frac{3}{4} \)
-
\( x = \frac{-9 - 15}{8} = \frac{-24}{8} = -3 \)
Thus, the zeros of the graph are \( \frac{3}{4} \) and \( -3 \).
The correct answer is:
A. \( \frac{3}{4} \) and \(-3\).
3 answers