Solving Quadratics Review

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial. It has the form: (a + b)² = a² + 2ab + b².

Front

Factor the expression: x² + 14x + 49

Back

(x + 7)²

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 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

How do you set a quadratic equation equal to zero?

Back

To set a quadratic equation equal to zero, rearrange the equation so that all terms are on one side, resulting in the form ax² + bx + c = 0.

Front

Factor the expression: 6x² - 7x - 10

Back

(6x + 5)(x - 2)

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = \frac{{-b \pm \sqrt{{b² - 4ac}}}}{{2a}}.

Front

Solve the quadratic equation: 2x² - 5x + 2 = 0

Back

x = \frac{1}{2} and x = 2

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation. It can be found using the formula: \left( -\frac{b}{2a}, f\left(-\frac{b}{2a}\right) \right).