Question bank: Quadratic Equation: Bhaskara

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Question 1:

Medium

An engineer is designing a ramp for a new skate park. He wants the ramp to have a parabolic shape, as he finds it aesthetically pleasing and also suitable for the skaters. The parabola he drew has a width of 4 meters at the base and a maximum height of 3 meters. He modeled this parabola using a second-degree equation: y = ax² + bx + c. If the vertex of this parabola is at the point (0, 3) and one of the zeros is at x = 2, how could you determine the coefficients a, b, and c of this equation?

Quadratic Equation: Bhaskara

Question 2:

Medium

In a rocket competition, a group of students used the quadratic equation to predict the maximum height their rocket would reach. According to their calculations, the height (h) of the rocket in meters, in relation to time (t) in seconds, is given by the function h(t) = -5t² + 30t + 2. What is the maximum height the rocket will reach and how long will it take for this to happen?

Quadratic Equation: Bhaskara

Question 3:

Easy

Quadratic Equation: Bhaskara

Question 4:

Medium

Carlos is planning to build a parabolic bridge over a river. The parabola that describes the shape of the bridge has the equation . Using the Bhaskara formula, determine the two possible intersections of this parabola with the x-axis.

Quadratic Equation: Bhaskara

Question 5:

Medium

A projectile is launched vertically upwards from the ground with an initial velocity of 50 m/s. The height of the projectile 'h' in meters, 't' seconds after the launch is given by the equation h(t) = 50t - 5t^2. Considering the situation described: 1. Calculate the time it takes for the projectile to reach the maximum height. 2. Determine the maximum height reached by the projectile. Use knowledge about the behavior of second-degree functions, the Bhaskara formula, and the characterization of the vertex of the parabola to solve the proposed questions.

Quadratic Equation: Bhaskara

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