Quadratic Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, 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.

Front

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

Back

The maximum height can be found using the formula t = -b/(2a) to find the time at which the maximum height occurs, then substituting this time back into the height equation.

Front

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

Back

The 'a' value 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 standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = 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 formula x = -b/(2a).

Front

How can you determine the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

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 real roots; if zero, one real root; if negative, no real roots.

Front

What is a projectile motion?

Back

Projectile motion is the motion of an object thrown into the air, subject to the force of gravity, and can be modeled by quadratic equations.

Front

How do you interpret the height of an object in a quadratic word problem?

Back

The height of an object in a quadratic word problem is typically represented by the variable h in the equation, which varies with time t.