Question

VERY URGENT

help tony hawk (located at T(-4,0)) reach the halfpipe (located at P (14,18)) by desigining a series of linear and quadratic relations that will form with a continous path from T to P. you must AVOID garbage cans at points a,b,c,d,e,f,g (your relations cant pass these points) you will be graphing and writing the equation of both linear and quadratic relations in order to create this route for tony hawk.

a) on a grid graph a path that includes
- one parabola that opens up
-one parabola that opens down
- one of these two parabolas must have a strech factor
- atleast two lines
-key points must be clearly labelled as an ordered pair and lie on major gridlines
-only need to state four equations
- label your garbage cans A(-3,1) B(8,6) c(0,5) d(4,14) e(14,13) f(11,15) g(3,7)
LABEL EVERYTHING (two parabolas, roots, vertex, endpoint, line segments)

2. for each quadratic equation, you cannot just state the equation, show all the steps!!
SEGMENT # : quadratic (opens up or down) (either vertex or standard form)
SEGMENT # : quadratic (opens opposite from above)(opposite form you chose above)
SEGMENT # : linear (cant be horizontal or vertical)
SEGMENT # : linear (no restrictions)

3. algebraically find the zeros to either one of the parabolas stated in the beginning. use any method.

Answer 1

The correct answer

Explanation:

To design a path for Tony Hawk from point T(-4,0) to the halfpipe at P(14,18) while avoiding the garbage cans at points A(-3,1), B(8,6), C(0,5), D(4,14), E(14,13), F(11,15), and G(3,7), we can use a combination of linear and quadratic relations.

1) Path description:

- Segment 1: Linear equation from T to A(B):

Line equation: y = mx + b

Calculate slope (m) = (y2 - y1) / (x2 - x1) = (1 - 0) / (-3 - (-4)) = 1

Calculate y-intercept (b): substitute the coordinates of point T

0 = 1*(-4) + b

b = 4

Line equation: y = x + 4

- Segment 2: Quadratic equation that opens up from A to C:

Parabola equation in vertex form: y = a(x - h)^2 + k

Find the vertex by taking the average of the x-coordinates of points A and C:

h = (x1 + x2) / 2 = (-3 + 0) / 2 = -3/2

Substitute the coordinates of A or C to find k:

1 = a(-3 - (-3/2))^2 + k

1 = a(0.5)^2 + k

1 = 0.25a + k

Choose a stretch factor (a) of 4 (for example)

Substitute k = 1 - 0.25a = 1 - 0.25(4) = 1 - 1 = 0

Parabola equation: y = 4(x + 3/2)^2

- Segment 3: Linear equation from C to D:

Line equation: y = mx + b

Calculate slope (m) = (y2 - y1) / (x2 - x1) = (14 - 5) / (4 - 0) = 9/4

Calculate y-intercept (b): substitute the coordinates of point D

14 = (9/4)(4) + b

14 = 9 + b

b = 14 - 9 = 5

Line equation: y = (9/4)x + 5

- Segment 4: Quadratic equation that opens down from D to F:

Parabola equation in vertex form: y = a(x - h)^2 + k

Find the vertex by taking the average of the x-coordinates of points D and F:

h = (x1 + x2) / 2 = (4 + 11) / 2 = 15/2

Substitute the coordinates of D or F to find k:

14 = a(4 - 15/2)^2 + k

14 = a(-7/2)^2 + k

14 = 49/4a + k

Choose a stretch factor (a) of -2 (for example)

Substitute k = 14 - 49/4a = 14 - 49/4(-2) = 14 + 49/2 = 14 + 24.5 = 38.5

Parabola equation: y = -2(x - 15/2)^2 + 38.5

- Segment 5: Linear equation from F to P:

Line equation: y = mx + b

Calculate slope (m) = (y2 - y1) / (x2 - x1) = (18 - 15) / (14 - 11) = 1

Calculate y-intercept (b): substitute the coordinates of point F

15 = 1(11) + b

b = 15 - 11 = 4

Line equation: y = x + 4

2) Equations for each segment:

- Segment 1: Linear equation from T to A(B):

Line equation: y = x + 4

- Segment 2: Quadratic equation that opens up from A to C:

Parabola equation: y = 4(x + 3/2)^2

- Segment 3: Linear equation from C to D:

Line equation: y = (9/4)x + 5

- Segment 4: Quadratic equation that opens down from D to F:

Parabola equation: y = -2(x - 15/2)^2 + 38.5

- Segment 5: Linear equation from F to P:

Line equation: y = x +