Interpreting Graphs of 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 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 can open upwards or downwards depending on the sign of the coefficient 'a'.

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 x = -b/(2a) for the function f(x) = ax² + bx + c.

Front

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

Back

The maximum height can be found by determining the vertex of the parabola, which occurs at x = -b/(2a) in the function h(t) = -16t² + vt + h0.

Front

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

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 significance of the y-intercept in 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, which gives the value c in f(x) = ax² + bx + c.

Front

How can you determine the time a projectile is above a certain height using a quadratic function?

Back

To find the time a projectile is above a certain height, set the height equation equal to that height and solve for t.

Front

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

Back

The height of an object in free fall can be modeled by the equation h(t) = -16t² + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant, given by 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 do you find the roots of a quadratic function?

Back

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