Using the 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).

Front

Identify A, B, and C in the equation: 10p² + 7p - 20 = 0

Back

A = 10, B = 7, C = -20.

Front

How do you complete the square for x² + 14x + ____?

Back

To complete the square, add (14/2)² = 49. The completed square is x² + 14x + 49.

Front

What are the solutions for the equation y = 2x² - 9x + 5 using the quadratic formula?

Back

The solutions are x = 3.9 and x = 0.6.

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 solutions; if = 0, one real solution; if < 0, no real solutions.

Front

What is the first step in using the quadratic formula?

Back

Identify the coefficients A, B, and C from the quadratic equation in standard form.

Front

Solve using the quadratic formula: 9x² = 4 + 7x. What is the first step?

Back

Rearrange to standard form: 9x² - 7x - 4 = 0.

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

How do you find the axis of symmetry for a quadratic equation?

Back

The axis of symmetry can be found using the formula x = -b/(2a).

Front

What is the significance of the leading coefficient (A) in a quadratic equation?

Back

The leading coefficient determines the direction of the parabola: if A > 0, it opens upwards; if A < 0, it opens downwards.