Which is the correct first step for using the Quadratic Formula to solve the quadratic below?

y=2x2+7x−15 (1 point)
Responses

−2±22−4(7)(−15)√2(7)the fraction with numerator negative 2 plus or minus square root of 2 squared minus 4 7 negative 15 end root and denominator 2 times 7

−7±72−4(2)(−15)√2(2)the fraction with numerator negative 7 plus or minus square root of 7 squared minus 4 2 negative 15 end root and denominator 2 times 2

−(−15)±(−15)2−4(2)(7)√2(−15)

1 answer

To solve the quadratic equation \( y = 2x^2 + 7x - 15 \) using the Quadratic Formula, we need to identify the coefficients of the quadratic equation in the standard form \( ax^2 + bx + c = 0 \). In this case, \( a = 2 \), \( b = 7 \), and \( c = -15 \).

The Quadratic Formula is given by:

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

Substituting the values of \( a \), \( b \), and \( c \):

  1. The numerator will be \( -b = -7 \).
  2. We need to compute the discriminant \( b^2 - 4ac = 7^2 - 4(2)(-15) = 49 + 120 = 169 \).
  3. The denominator will be \( 2a = 2(2) = 4 \).

So, the correct first step using the Quadratic Formula will use \( -7 \) in the numerator.

Therefore, the correct response is:

−7±√72−4(2)(−15)the fraction with numerator negative 7 plus or minus square root of 7 squared minus 4 times 2 times negative 15 end root and denominator 2 times 2.