Solving Quadratic Equations

Front

What is the standard form of a quadratic equation?

Back

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

Front

True or False: The quadratic formula can be used to solve quadratic equations that cannot be factored.

Back

True

Front

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

Back

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

Front

Solve by completing the square: x² − 10x - 11 = 0.

Back

x = −1 and 11

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 is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

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 roots; if = 0, one real root; if < 0, no real roots.

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 in standard form?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

What is the effect of the coefficient 'a' in a quadratic equation?

Back

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