4.5/4.6 Quadratic Formula Completing the Square

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

Identify the values of a, b, and c in the equation: 4x² - 8x - 3 = 0.

Back

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

Front

What is the quadratic formula?

Back

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

Front

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

Back

The discriminant indicates the number and type of solutions: if > 0, two real solutions; if = 0, one real solution; if < 0, no real solutions.

Front

How do you complete the square for the equation x² + 6x + 5 = 0?

Back

To complete the square, rewrite as (x + 3)² - 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 can you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, found using x = -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) that divides the parabola into two mirror-image halves.

Front

Given the function h(t) = -5t² + 20t + 25, how do you find when the balloon hits the ground?

Back

Set h(t) = 0 and solve for t: -5t² + 20t + 25 = 0.

Front

What is the significance 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.