Master essential math concepts and problem-solving skills tested on the New SAT without the use of a calculator.
Quadratic equations, in the form \( ax^2 + bx + c = 0 \), show up often on the SAT. You can solve them by factoring, completing the square, or using the quadratic formula.
Factoring means rewriting the quadratic as a product of two binomials. Look for two numbers that multiply to \( ac \) and add to \( b \).
If factoring is tough, use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Quadratics model projectile motion, area problems, and more.
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]
Solve \( x^2 - 5x + 6 = 0 \) by factoring: \( (x-2)(x-3) = 0 \), so \( x = 2 \) or \( x = 3 \).
Use the quadratic formula for \( 2x^2 + 3x - 2 = 0 \).
Quadratic equations describe parabolic relationships and can be solved by several techniques.