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 parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (opening upwards or downwards).

Front

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

Back

The maximum height can be found by calculating the vertex of the quadratic function, using the formula t = -b/(2a) to find the time at which the maximum height occurs.

Front

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

Back

The coefficient 'a' determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How can you determine the time it takes for an object to hit the ground using a quadratic function?

Back

To determine the time it takes for an object to hit the ground, set the height function equal to zero and solve for t.

Front

What is the formula for the maximum profit in a quadratic profit function?

Back

The maximum profit can be found at the vertex of the profit function, using the formula x = -b/(2a) to find the price that maximizes profit.

Front

What does the discriminant of a quadratic equation tell us?

Back

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

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).

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, and intercepts, then plot these points and draw a smooth curve through them.