Someone, please help!
Kelly is on the football field at the 4-yard line and she fires her tomato cannon (which is on the ground). When the tomato is over the 6-yard line, the potato is 56 yards in the air. The tomato lands on the 20-yard line and explodes.
a) Create an equation for this situation.
Let y = the altitude of the tomato (yards).
Let x = the horizontal distance along the football field (yards).
b) How high in the air does the tomato get?
c) What would be a reasonable domain and range for the graph in this situation? Explain.
Answers
Answer:
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Step-by-step explanation:
Answer:
a) y = -2(x-4)(x-20)
b) The tomato would be 128 yards in the air.
c) Domain: (4,20)
Range: (0, 128)
Step-by-step explanation:
a) The equation is in factored form, because it was the easiest equation to create given the information. You can also write it in standard form, but since the problem didn't specifically state how to write the equation, it probably does not matter as much. The equation for factored form is y = a(x-r1)(x-r2), where r1 and r2 are the x-intercepts. Since we know the x-intercepts are 4 and 20, we can plug it in the equation. A is also known as the "stretch factor". It makes the parabola wider or thinner. We can find out the "stretch factor" using the point (6,56). The information tells us that (6,56) is on the parabola. If we use y = -(x-4)(x-20), (6,56) will not be on the parabola. Therefore, our equation is y = -2(x-4)(x-20). In standard form, it would be: y = -2x^2 + 48x - 160.
b) The highest point (or lowest, depending on the direction of the parabola) on a parabola is the vertex. This is when our equation comes in handy. We can easily find the x-coordinate of the parabola, because it's on the axis of symmetry, which is x = 12. (We add the x-intercepts and divide by 2 to find the axis of symmetry.) To find the y-coordinate, we can plug in 12 into the equation.
y = -2(x-4)(x-20) ---> -2(12-4)(12-20) = 128
c) The domain would be (4,20), because (4,0) is where the tomato cannon was fired and (20,0) was where the tomato exploded. The range is (0, 128). The range is the set of possible y-values. If 0 is the ground, the tomato wouldn't be able to go through the ground and become negative. Also, 128 yards is the highest the tomato went up in the air. The lowest and highest the tomato went is 0 and 128.
(Note: I'm not 100% sure if this is correct at all and I'm not very good at explaining things, so I apologize ><)