Quadratic Word Problems

Front

What is a quadratic function?

Back

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

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the quadratic equation ax² + bx + c.

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).

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, which can be calculated using the vertex formula. For a function in standard form, it is f(-b/(2a)).

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.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola. A larger |a| value makes the parabola narrower.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x - p)(x - q) = 0, then set each factor equal to zero to find the solutions x = p and x = q.

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.