Solving Quadratics and Quadratic Formula

Front

What is a quadratic equation?

Back

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

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

How do you convert a quadratic equation to standard form?

Back

To convert to standard form, rearrange the equation to the form ax² + bx + c = 0 by moving all terms to one side.

Front

Solve for x: 2x² + 7x - 15 = 0

Back

x = -5 and x = 1.5.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

n = 4 and n = 5.

Tags

CCSS.HSA-REI.B.4B

Front

Solve for x. Round to the nearest hundredth if necessary: 3x² = 16x + 12

Back

x = -0.67 and x = 6.

Tags

CCSS.HSA-REI.B.4B

Front

Identify a, b, and c in the equation: 4x² - 8x = 3

Back

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

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.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror images.