Solving Quadratics and 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

Solve using the quadratic formula: 2x² - 9x - 35 = 0

Back

x = -5/2 and x = 7

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

Solve for x: 2x² = -x + 3

Back

x = -1.5 and x = 1

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Solve: 2x² + 7x - 15 = 0

Back

x = -5 and x = 1.5

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

Solve for x: 3x² = 16x + 12

Back

x = -0.67 and x = 6

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. It can be found using the formula x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.