Front

What are x-intercepts?

Back

The x-intercepts of a function are the points where the graph intersects the x-axis, meaning the value of y is 0.

Front

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

Back

To find the maximum height of a quadratic function in the form h(t) = at^2 + bt + c, use the formula t = -b/(2a) to find the time at which the maximum height occurs.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What does the equation h(t) = -5t^2 + 40t + 2 represent?

Back

This equation represents the height of a water balloon launched into the air, where h(t) is the height at time t.

Front

How do you determine the height from which an object is launched?

Back

The height from which an object is launched can be found by evaluating the function at t=0.

Front

What is the significance of the coefficient of t^2 in a quadratic equation?

Back

The coefficient of t^2 determines the direction of the parabola: if it is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the formula for the height of a projectile?

Back

The height of a projectile can be modeled by the equation h(t) = -gt^2 + vt + h0, where g is the acceleration due to gravity, v is the initial velocity, and h0 is the initial height.

Front

How do you find when an object hits the ground using a quadratic equation?

Back

To find when an object hits the ground, set the height equation equal to zero and solve for t.

Front

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

Back

Maximum height refers to the highest point reached by the projectile during its flight.

Front

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

Back

The discriminant (b^2 - 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.