Solving Quadratics and Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

Identify the values of a, b, and c in the equation 4x² - 8x - 3 = 0.

Back

a = 4, b = -8, c = -3.

Front

Solve using the quadratic formula: x² + 4x - 40 = -8.

Back

x = -8 and x = 4.

Front

Use the quadratic formula to solve: n² = 9n - 20.

Back

n = 4 and n = 5.

Front

Solve by factoring: x² - 9x + 20 = 0.

Back

x = 4 and x = 5.

Front

What is the zero product property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a ≠ 0.

Front

How do you convert a quadratic equation to standard form?

Back

Rearrange the equation to the form ax² + bx + c = 0.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).