Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What are the values of a, b, and c in the equation 2x² + 7x - 15 = 0?

Back

a = 2, b = 7, c = -15.

Front

Solve using the Quadratic Formula: 2x² + 7x - 15 = 0

Back

x = -5 or x = 1.5.

Tags

CCSS.HSA-REI.B.4B

Front

What is the first step in using the Quadratic Formula?

Back

Identify the coefficients a, b, and c from the quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant (b² - 4ac) tell us?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

How do you convert the equation 4x² - 8x = 3 to standard form?

Back

Subtract 3 from both sides to get 4x² - 8x - 3 = 0.

Front

What are the values of a, b, and c in the equation 4x² - 8x - 3 = 0?

Back

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

Front

Use the quadratic formula to find the solutions for y = -x² - 5x + 12.

Back

x = -6.77 and x = 1.77.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the quadratic formula in solving quadratic equations?

Back

It provides a systematic method to find the roots of any quadratic equation.

Tags

CCSS.HSA-REI.B.4B

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.