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 vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

How do you find the maximum profit from a quadratic profit function?

Back

To find the maximum profit, use the vertex formula x = -b/(2a) to find the price that maximizes profit, then substitute x back into the profit function.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How can you determine when an object hits the ground using a quadratic function?

Back

Set the height function equal to zero and solve for t to find when the object reaches a height of zero (ground level).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

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

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.

Front

What does the 'a' value in a quadratic function indicate about the graph?

Back

The 'a' value indicates the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

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 formula x = -b/(2a).