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

Back

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

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 on each side.

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

True or False: The quadratic formula can be used to solve any quadratic equation.

Back

True.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you convert the equation y = -x² - 5x + 12 into standard form?

Back

Rearrange it to -x² - 5x + 12 = 0.

Front

What is the vertex of a parabola represented by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a).

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.