Solving Quadratic Equations

Front

What does it mean if the graph of a quadratic does not intercept the x-axis?

Back

It has No Real Solution.

Front

Solve by using square roots: -5x^2 = -50

Back

x = ± √10

Front

Solve by using square roots: x^2 - 24 = 0

Back

x = ± 2√6

Front

Solve the quadratic equation by completing the square: x^2 + 4x + 1 = 0

Back

x = -2 ± √3

Front

Identify the values of a, b, and c in the quadratic equation: 4x^2 - 8x = 3

Back

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

Front

What is a quadratic equation?

Back

An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the quadratic formula?

Back

x = (-b ± √(b^2 - 4ac)) / (2a) for the equation ax^2 + bx + c = 0.

Front

What does the discriminant (b^2 - 4ac) tell us about a quadratic equation?

Back

It determines the nature of the roots: if > 0, 2 real solutions; = 0, 1 real solution; < 0, no real solutions.

Front

What is completing the square?

Back

A method to solve quadratic equations by rewriting them in the form (x - p)^2 = q.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.