Question

what are the zeros of the graph of y= 2x^2 + 5x -12

Answer 1

To find the zeros of the quadratic function \( y = 2x^2 + 5x - 12 \), we need to solve the equation \( 2x^2 + 5x - 12 = 0 \).

We can use the quadratic formula:

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

Where \( a = 2 \), \( b = 5 \), and \( c = -12 \).

1. Calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot (-12) = 25 + 96 = 121
\]

2. Substitute \( a \), \( b \), and the discriminant into the quadratic formula:

\[
x = \frac{-5 \pm \sqrt{121}}{2 \cdot 2}
\]

\[
x = \frac{-5 \pm 11}{4}
\]

3. Calculate the two potential solutions:

- For the positive case:

\[
x = \frac{-5 + 11}{4} = \frac{6}{4} = \frac{3}{2}
\]

- For the negative case:

\[
x = \frac{-5 - 11}{4} = \frac{-16}{4} = -4
\]

Thus, the zeros of the graph are:

\[
x = \frac{3}{2} \quad \text{and} \quad x = -4
\]