Modeling With Quadratic Functions

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.

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 vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

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

Back

The 'a' value determines the direction of the parabola's opening: 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).

Front

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

Back

To find the maximum height, calculate the vertex of the parabola using the formula h = -16t² + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

What is the Y-intercept of a quadratic function?

Back

The Y-intercept is the point where the graph intersects the Y-axis, found by evaluating the function at x = 0.

Front

What does the term 'maximum height' refer to in projectile motion?

Back

Maximum height refers to the highest point reached by an object in motion, represented by the vertex of the quadratic function.

Front

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

Back

Set the height function equal to zero and solve for time (t) to find when the projectile reaches ground level.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape.