Question

1. The equation y=x^2-9x+20 models the roller coasters 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 represent the amount of time (in seconds) since the ride began.
Part 1: write the equation in factored form.



Part 2: 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 of use the first part of the quadratic Formula (x=-b)
——
2a

Part 3: what is the y-intercept? Use the equation y=x^2-9x+20


Part 4: Sketch the graph of y=x^2-9x+20. Identify the vertex and x- and y-intercepts on your sketch




Part5: use the graph to answer the questions.

A. Between what times does the roller coaster dip below the platform?

B. What is the height and time at which Erin picture is taken during the roller coaster ride?

C. Erin picture is taken at the lowest point of the roller coaster.


35points!! To whoever help me with this.

Answer 1

Answer:

1) the factored form is  y= ( x-5 ) ( x+4 )

2) the vertex is (4.5, -0.25)

3) the y intercept is when x equals 0 so it is at (0,20)

4) it opens upward and the vertex is (4.5, -0.25) the x intercepts are (4,0) and (5,0) and the y intercept is  (0,20)

5)

a. it dips  between 4 seconds and 5 seconds so the x intercepts are (4,0) and (5,0)

b. it is taken at the vertex aka the lowest point so the height is -0.25

Answer 2

Answer:

Part 1:

$y= (x-4)(x-5)$

Part 2:

$(\frac{9}{2}, - \frac{1}{4})$

Part 3:

$Y=20$

Part 5:

The height:

$-\frac{1}{4}$

The time:

$\frac{9}{2}$s

Step-by-step explanation:

$y = x^{2} -9x+20$ Is a quadratic equation.

Part 1:

We use $x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}$ to factor quadratic equations

$y = x^{2} -9x+20$

a=1 b=-9 c=20

$x = \frac {-(-9) \pm \sqrt {(-9)^2 - 4(1)(20)}}{2(1)}$

$x = \frac {9 \pm \sqrt {81 -80}}{2}$

$x = \frac {9 \pm {1}}{2}$

we solve both possibilities

$x = \frac {9 + {1}}{2}=5$

$x = 5$  

$x = \frac {9 -{1}}{2}=4$

$x=4$

The factored form would be

$y= (x-4)(x-5)$

Part 2:

We use the formula to find the x coordinate of the vertex of a parabola

$V_{x}=\frac{-b}{2a}$

$y = x^{2} -9x+20$

a=1 b=-9 c=20

$V_{x}=\frac{9}{2}$

Now we substitute the value of x in $y = x^{2} -9x+20$ to find the value of the coordinate y of the vertex

$y = \ (\frac{9}{2} )^{2} -9(\frac{9}{2}) +20\\ y= \frac{81}{4} -\frac{81}{2} +20\\ y= -\frac{1}{4}$

The vertex of the parabola is

Vertex:

$(\frac{9}{2}, - \frac{1}{4})$

Part 3:

the y-intercept is when the value of x = 0.

We substitute this value in $y = x^{2} -9x+20$

$y = 0^{2} -9(0)+20= 20$

The y-intercept is $y=20$

Part 5:

A.

Between 4s and 5s

B and C.

Erin's photograph is taken at the lowest point of the roller coaster.

The lowest point of the parabola is the vertex.

The coordinate y of the vertex gives us the height and the coordinate x the time.

The height:

$-\frac{1}{4}$

It is negative because it is below the point we take as zero.

The time:

$\frac{9}{2}$s

Part 4:

The answer is the graph

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