Football Lesson 5.1
1. y= -0.035x^2 + 1.4x + 1, where x is the distance (in yards) and y is the height (in yards)
a. Does the graph open up or down?
b. Does the graph have a Maximum value or a minimum value?
c. graph the quadratic function.
(i'll graph it just write it in the formula)
d. find the maximum height
2. y= -0.088x^2 + 2.5x +1where x is the distance (in yards) and y is the height (in yards)
a. graph the quadratic function
b. Find the greatest height
c. If the punter punted the ball from the 40-yards line, did theball reach the endzone?
3. y=-0.00545x^2 + 1.145x
a. Find the distance the stone traveled.
b. Find the maximum height of the stone
4. y=-0.0044x^2 + 1.68x
a. The height of the wall is 120 yards
b. The height of the wall is 100 ft
Football Lesson 5.1
1. y= -0.035x^2 + 1.4x + 1, where x is the distance (in yards) and y is the height (in yards)
a. Does the graph open up or down?
b. Does the graph have a Maximum value or a minimum value?
c. graph the quadratic function.
(i'll graph it just write it in the formula)
d. find the maximum height
2. y= -0.088x^2 + 2.5x +1where x is the distance (in yards) and y is the height (in yards)
a. graph the quadratic function
b. Find the greatest height
c. If the punter punted the ball from the 40-yards line, did theball reach the endzone?
3. y=-0.00545x^2 + 1.145x
a. Find the distance the stone traveled.
b. Find the maximum height of the stone
4. y=-0.0044x^2 + 1.68x
a. The height of the wall is 120 yards
b. The height of the wall is 100 ft
To solve these problems involving quadratic functions, we need to understand the general form of a quadratic equation, which is written as y = ax^2 + bx + c. In this case, y represents the height and x represents the distance.
1.
a. To determine whether the graph opens up or down, we look at the coefficient of the x^2 term. In this case, the coefficient is -0.035. Since it is negative, the graph opens downwards.
b. To find the maximum or minimum value of the graph, we need to consider the coefficient of the x^2 term. Since the coefficient is negative (-0.035), the graph has a maximum value.
c. To graph the quadratic function, we can plot points. You can substitute x values in the equation and calculate the corresponding y values. For example, if we choose x = 0, then y = 1. Next, choose some other values for x and calculate the corresponding y values. Plot these points on a graph and connect them to form a parabolic shape.
d. To find the maximum height, we can use the formula for the x-coordinate of the vertex: x = -b / (2a). Plugging in the values, we get x = -1.4 / (2 * -0.035) = 20. The maximum height occurs at x = 20, so substitute this value into the equation to find the corresponding y value.
2.
a. To graph the quadratic function, we can follow the same process as in the previous question.
b. To find the greatest height, we need to find the maximum point of the graph. This can be done by finding the x-coordinate of the vertex using the formula: x = -b / (2a). Plugging in the values, we get x = -2.5 / (2 * -0.088) = 14.20. Substitute this value into the equation to find the corresponding y value.
c. To check if the ball reaches the endzone, we need to compare the distance covered by the ball (x value) with the distance to the endzone. If the x value is greater than or equal to the distance to the endzone, then the ball reached the endzone.
3.
a. The distance the stone traveled can be found by finding the x-intercepts of the graph. This means we need to solve the equation y = 0. Set the equation equal to zero and solve for x. The x-values obtained from the solutions will give us the points where the ball reaches the ground.
b. To find the maximum height of the stone, we can use the formula for the x-coordinate of the vertex: x = -b / (2a). Plugging in the values, we get x = -1.145 / (2 * -0.00545). Substitute this value into the equation to find the corresponding y value.
4.
a. To find the point at which the height of the wall is 120 yards, we need to set y = 120 in the equation and solve for x.
b. To find the point at which the height of the wall is 100 ft, we need to convert 100 ft to yards (1 yard = 3 ft) and set y = 100 / 3 in the equation. Then solve for x.