Quadratic Applications

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written 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 (-b/2a, f(-b/2a)).

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 roots of a quadratic equation?

Back

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

Front

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

Back

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

Front

What is the maximum height in a quadratic application problem?

Back

The maximum height is the vertex of the parabola when modeling a projectile's motion, representing the highest point reached.

Front

How do you determine the time of flight in a projectile motion problem?

Back

The time of flight can be found by determining when the height function equals zero, indicating when the object hits the ground.

Front

What is the formula for the height of an object in free fall?

Back

The height can be modeled by the equation h(t) = -16t² + h₀, where h₀ is the initial height in feet.

Front

How do you model the height of an object thrown upwards?

Back

The height can be modeled by the equation h(t) = -at² + vt + h₀, where a is the acceleration due to gravity, v is the initial velocity, and h₀ is the initial height.