Question

1. $-2x^{2}+4x + 30$

a = __ b = c = ___
substitute into the quadratic formula:

what are the x - intercepts?

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), given \(-2x^2 + 4x + 30\), so \(a = -2\), \(b = 4\), \(c = 30\).

Step2: Quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute \(a=-2\), \(b = 4\), \(c = 30\):
\(x=\frac{-4\pm\sqrt{4^2-4\times(-2)\times30}}{2\times(-2)}\)

Step3: Calculate discriminant

Calculate \(b^2 - 4ac\):
\(4^2-4\times(-2)\times30=16 + 240=256\)

Step4: Simplify square root

\(\sqrt{256}=16\)

Step5: Solve for x

\(x=\frac{-4\pm16}{-4}\)
Case 1: \(x=\frac{-4 + 16}{-4}=\frac{12}{-4}=-3\)
Case 2: \(x=\frac{-4-16}{-4}=\frac{-20}{-4}=5\)

Answer:

\(a=-2\), \(b = 4\), \(c = 30\); The \(x\)-intercepts are \(x=-3\) and \(x = 5\)