Algebra 1 benchmark

Question

The equation below describes a function that models the height of a football thrown by a player. In the equation below, y represents the height of the football, in feet, and x represents the time the football is in the air, in seconds.

У = - 16x2 + 48x + 6

After _____ seconds, the ball reaches its maximum height.

Answer 1

Looking at the formula, this is a quadratic equation, making a parabola, specifically an upside down or a negative parabola. This shape sorta looks like the path of throwing something. The y value of the parabola, is telling us about the height. Since we want the maximum height, we want to know where is y the highest. Thinking back to parabola terminology, we want to know the vertex. The x value of the vertex tells us the time we reach that maximum. The y tells us how high is the maximum. You can use any method you prefer to get the vertex. I like using the vertex formula. You can graph it or if your teacher allows calculators, it is up to you, but I will show how to use the vertex formula.

The h (the x value of a parabola's vertex) is given by the following formula: -b/(2a)

Our equation is y = -16x² + 48x + 6

b = 48

a = -16

Plug it in:

-48/(2*-16) = -48/-32 = 1.5 The negatives cancel, and we are left with 1.5 seconds

The math, other than memorizing the vertex formula, is multiplication and division. But more importantly I hope you can understand what's going on with the equation, why we want the vertex, and what all the variables mean. This type of problem is pretty common, so understanding it would help you a lot in your journey through quadratic word problems.