4.5 Solving Quadratic Equations Lesson Check

Front

What are the zeros, roots, and solutions of a quadratic equation?

Back

The zeros, roots, and solutions of a quadratic equation are the values of x that make the equation equal to zero. They represent the x-intercepts of the graph of the quadratic function.

Front

Solve the quadratic equation: x^2 - 49 = 0

Back

x = -7, x = 7

Front

Solve the quadratic equation: (x - 9)(x + 3) = 0

Back

x = -3 or x = 9

Front

True or False: The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

Back

True

Front

What is the first step to solve the equation x^2 + 6x = 5 using the quadratic formula?

Back

Subtract 5 from both sides to set the equation to zero.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

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

Back

The discriminant indicates the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are two complex roots.

Front

How do you factor a quadratic equation in the form x^2 + bx + c?

Back

To factor, find two numbers that multiply to c and add to b, then express the quadratic as (x + p)(x + q) where p and q are those numbers.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) where h = -b/(2a) and k is the function value at h.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).