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 'a' value in the quadratic equation: y = 16x² - 8x - 24.

Back

The 'a' value is 16.

Front

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

Back

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

Front

What is the value of 'c' in the equation: x² + 2x = 6?

Back

The value of 'c' is -6.

Front

Determine the values of a, b, and c for the quadratic 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

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 vertex of a quadratic function given in standard form?

Back

The vertex can be found using the formula h = -b/(2a) and then substituting h back into the equation to find 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 images.

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.