Quadratic Functions 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 can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you find the maximum height of an object modeled by a quadratic function?

Back

The maximum height can be found by calculating the vertex of the parabola using the formula t = -b/(2a) and then substituting this value back into the function.

Front

What is the formula to find the time when a projectile hits the ground?

Back

Set the height function h(t) = 0 and solve for t using the quadratic formula.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) are the values of x for which the function f(x) = 0, representing the points where the graph intersects the x-axis.

Front

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

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

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 determine if a quadratic function has a maximum or minimum?

Back

If 'a' is positive, the function has a minimum; if 'a' is negative, the function has a maximum.

Front

What is the standard form of a quadratic function?

Back

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