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

Back

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

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

Front

Solve for x using the quadratic formula: 2x² + 4x - 6 = 0.

Back

x = (-4 ± √(4² - 4*2*(-6))) / (2*2) = (-4 ± √(16 + 48)) / 4 = (-4 ± √64) / 4 = (-4 ± 8) / 4. Solutions: x = 1 or x = -3.

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

Identify the 'c' value in the equation: y = 16x² - 8x - 24.

Back

c = -24.

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 from standard form to vertex form?

Back

Complete the square on the quadratic equation to express it in the form y = a(x - h)² + k.

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

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.