Final answer:
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.