Question

Using the Quadratic Formula, solve for the zeros of the following standard form parabola and rewrite the equation in factored form. Solve the equation by simplifying the fractions and square root, but you may express your factored form equation using decimals for the values of p and q.

y = 2x^2 + 4x - 9.

Answer 1

To solve the quadratic equation y = 2x^2 + 4x - 9 using the Quadratic Formula, substitute the values of a, b, and c into the formula. Simplify the expression inside the square root and solve for x by calculating the two possible values. Rewrite the equation in factored form by factoring out the quadratic expression.

Step-by-step explanation:

To solve the quadratic equation y = 2x^2 + 4x - 9, we can use the Quadratic Formula. The formula is used for equations in the form ax^2 + bx + c = 0. Comparing the given equation to the standard form, we have a = 2, b = 4, and c = -9.

Substituting the values into the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), we get x = (-4 ± √(4^2 - 4(2)(-9))) / (2(2)).

Simplifying the expression inside the square root, we have x = (-4 ± √(16 + 72)) / 4, which further simplifies to x = (-4 ± √(88)) / 4.

Finally, we can rewrite the equation in factored form by factoring out the quadratic expression: y = 2(x - p)(x - q), where p and q are the zeros obtained from the quadratic formula.