Question

Please help ?

Answer 1

At the state fair, Erin and her cousin ride the Ultra Drop roller coaster. When the ride plummets down the first hill, it dips below the loading platform. At the bottom, a camera snaps the riders' picture before hurtling them back toward the sky.
The equation y=x^2-9x+20 models the roller coaster's path over time. The variable y represents height (in feet) above or below the platform. At y=0, the roller coaster is even with the platform. The variable x represents the amount of time (in seconds) since the ride began.
Factor and graph the equation to Better understand Erin's ride.
Part1: write the equation in factored form.


Part2: find the vertex of the parabola. Hint: to find the x-value of the vertex , take the average of the x-values of the x-intercepts or use the first part of the quadratic formula (x=-b/2a).

Part3: identify the intercepts
A.what are the x-intercepts ? Hint: use the equation from part 1.

B. What is the y-intercept? Hint: use the equation y=x^2-9x+20.

Part4: sketch the graph of y=x^2-9x+20. Identify the vertex and x-intercepts on your sketch.

Answer 2

@1davey29

Answer 3

Part 1: write this
y= x^2 -9x + 20 in factored form
Do you know how to do that? Finding the GCF and all that?

Answer 4

What do you mean ? Like find the factors that go into 9 and 20 ? @Will.H

Answer 5

Factored form is the factors needed to make a polynomial. Ex. y=x^2-5x-14 can be factored into (x+2) and (x-7), so your factored form would be (x+2)(x-7). I G2G for now, but will be back in about 30 mins. If anybody else wants to lead on from here, feel free to.

Answer 6

So it would be like (x+2) (x-5) ?

Answer 7

@1davey29

Answer 8

@jackthegreatest

Answer 9

Sorry for being late. Your polynomial is set up as ax^2+bx+c, so you need to find what adds to b and multiplies to a*c. In your case, you have 1x^2+-9x+20, so you have to add to -9 and multiply to 20*1. Your numbers here would be -4 and -5, so you would have (x-4)(x-5) as your factored form

Answer 10

Part 2) The x coordinate of the vertex is equal to -b/2a, as you have in the question. Your b and a will come from your expanded equation of the parabola. In this case, y=x^2-9x+20, your a is 1 and your b is -9, so your x coordinate will be x=-b/2a=-(-9)/2(1)=9/2=4.5. To find the y coordinate, just plug in the x coordinate into your equation of the parabola, so y=x^2-9x+20=(4.5)^2-9(4.5)+20=20.25-40.5+20=-0.25, which is -1/4 in fraction form. So your vertex would be at (9/2,-1.4) or (4.5,-0.25), depending if you want it by decimals or fractions.

Answer 11

Part 3a) Your x-intercepts can be found by solving for x in each of your factors from your factored form, so (x-4)(x-5) means x=4 and x=5. For an x-intercept, y will always equal 0, so your x-intercepts will be (4,0) and (5,0)

Answer 12

Part 3b) To find your y-intercept, just set x equal to 0 in your equation, so in this case, it would equal 20, so your coordinates would be (0,20)

Answer 13

For part 4, just draw the graph and label the points you found above.