Quadratics in Context In Class Practice

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 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 x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set f(x) = 0 and solve the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

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

Back

The maximum height refers to the highest point reached by an object in projectile motion, which can be found at the vertex of the corresponding quadratic function.

Front

How can you determine the time it takes for a projectile to reach its maximum height?

Back

The time to reach maximum height can be found using the formula t = -b/(2a) from the vertex form of the quadratic function.

Front

What is the formula for the height of an object in projectile motion?

Back

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

Front

What does f(3) = 246 mean in the context of a baseball's height function?

Back

f(3) = 246 means that after 3 seconds, the baseball is 246 feet in the air.

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 interpret the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, representing the value of the function when x = 0.