4.1-4.3 flashcard

Front

Solve for the values of x: (x - 5)(x - 1) = 0

Back

x = 5 or x = 1

Front

What is the axis of symmetry for the graph of a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. For the parabola y = ax^2 + bx + c, the axis of symmetry is given by x = -b/(2a).

Front

Solve for x: x^2 = 64

Back

x = 8 or x = -8

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. For the parabola in standard form y = a(x - h)^2 + k, the vertex is (h, k).

Front

Solve for h: (h - 2)^2 = 9

Back

h = 5 or h = -1

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0. It is given by x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What does it mean for a quadratic equation to have real solutions?

Back

A quadratic equation has real solutions if the discriminant (b^2 - 4ac) is greater than or equal to zero.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found by factoring, using the quadratic formula, or completing the square.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.