Question

which is the correct first step for using the quadratic formula to solve the quadratic below? (1 point)
y = 5x² - 2x + 6
options:
-6±√(6² - 4(-2)(5)) / (2(-2))
-5±√(5² - 4(6)(-2)) / (2(6))
-(-2)±√((-2)² - 4(5)(6)) / (2(5))

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) for a quadratic equation \( ax^2 + bx + c = 0 \). First, we need to identify \( a \), \( b \), and \( c \) from the given quadratic \( y = 5x^2 - 2x + 6 \). For solving for \( x \) (when \( y = 0 \), the standard quadratic equation form is \( 5x^2 - 2x + 6 = 0 \)), so \( a = 5 \), \( b = -2 \), \( c = 6 \).

Step2: Substitute into Quadratic Formula

Substitute \( a = 5 \), \( b = -2 \), \( c = 6 \) into the quadratic formula. The numerator's first part is \( -b \), which is \( -(-2) \), the discriminant is \( b^2 - 4ac = (-2)^2 - 4(5)(6) \), and the denominator is \( 2a = 2(5) \). So the expression should be \( \frac{-(-2) \pm \sqrt{(-2)^2 - 4(5)(6)}}{2(5)} \), which matches the third option.

Answer:

The third option (the one with \( \frac{-(-2) \pm \sqrt{(-2)^2 - 4(5)(6)}}{2(5)} \))