A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 10 mm halfway across a horizontal
distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)

A parabola is a mirror-symmetrical U-shape.

From the question, we have:

[tex]\mathbf{Vertex: (h,k) = (80,10)}[/tex]

[tex]\mathbf{Origin: (x,y) = (0,0)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Substitute the values of origin and vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{0 = a(0 - 80)^2 + 10}[/tex]

[tex]\mathbf{0 = a(- 80)^2 + 10}[/tex]

[tex]\mathbf{0 = 6400a + 10}[/tex]

Collect like terms

[tex]\mathbf{6400a =- 10}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{640}}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

The focus of a parabola is:

[tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

[tex]\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}[/tex]

[tex]\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}[/tex]

[tex]\mathbf{Focus = (80, -11\times 160)}[/tex]

[tex]\mathbf{Focus = (80, -1760)}[/tex]

The equation of the directrix is:

[tex]\mathbf{y = -a}[/tex]

So, we have:

[tex]\mathbf{y = \frac{1}{640}}[/tex] ----- the directrix

The axis of symmetry is:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

We have:

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}[/tex]

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }[/tex]

A quadratic function is represented as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

So, we have:

[tex]\mathbf{a = -\frac{1}{640}}[/tex]

[tex]\mathbf{b = \frac{1}{4}}[/tex]

Recall that:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

So, we have:

[tex]\mathbf{x = -\frac{1/4}{2 \times -1/640}}[/tex]

[tex]\mathbf{x = \frac{1/4}{1/320}}[/tex]

This gives

[tex]\mathbf{x = \frac{320}{4}}[/tex]

[tex]\mathbf{x = 80}[/tex]

Hence, the axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]

Read more about parabola at:

https://brainly.com/question/21685473

I need help pleaseeeee
No links

Solve for the unknown.​

A teacher tells her students she is just over 1 and billion seconds old.
1. Write her age in seconds using scientific notation.

A radio station requires DJs to play 2 commercials for every 10 songs they play. What is the unit rate of songs to commercials.​

PLEASE HELP WILL MARK BRAINLIEST TO BEST ANSWER

I need help pleaseeeee

2)
Where is the opposite of -10 located on a number line?
ght
X
A)
to the left of o
he
ning
1.28
Cools
B)
to the right of 0
C)
to the right of 12
D
to the left of -10?

Andy is scuba diving. He starts at sea level and then descends 10 feet in 2 1/2 minutes.

Part A. How would you represent Andy’s descent as a unit rate ? Express your answer in an integer.

Part B.If he continues at this rate , where will Andy be in relation to sea level after 6 minutes?

Write the equation of the parabola in vertex form.
vertex (3,1), point (2, - 4).
f(x)=
)
w

t (x) = 5x^2- 3x+4, what is the value t (-3)?

Work out the value of 3.14

hey uhm can someone answer this for 12 points

Find the equation in slope-intercept form that describes line.
A line through (-1, 1) and (2,3)

70+2e+3e=180° answere me ​

Solve: (x - y)/(sqrt(x) + 1) = 2 + (sqrt(x) - 5)/3​

HELPOOPPPOOPFOLFMTMR ME

You’ve decided to open a checking account. You know there are a number of differences with individual banking institutions. Name at least 3 good questions to ask to get started, and explain why knowing this information is helpful. Use complete sentences.

Given: WX congruent yz
Prove: WYXZ

Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with
multiplicity 2?
Of(x) = 2(x + 7)(x + 5)(x - 2)
Of(x) = 2(x-7)(x - 5)(x + 2)
Of(x) = (x + 7)(x + 5)(x + 5)(x - 2)
of(x) = (x-7)(x-5)(x - 5)(x + 2)
Mark this and return
Save and Exit
Next
Sb

7
10 points
One force of magnitude 48 acts on an object. Another force of magnitude 90 acts on the object at a right angle, what is the magnitude of the resultant force on the object?
Type your answer...

maths giving 10 point asap 1 question only





Find the value of P​

HELP PLEASEEEEEEE!!!!

Tìm hàm số bậc nhất,biết đồ thị đi qua điểm (3;−2), song song với đường thẳng

′:3−2+1=0

PLEASE HELP!!! 20 POINTS

Justify each step of the solution by stating the property that was used to get to each step.

Given: 2(10 − 13)+ 9 −5 = −34 + 55

Step 1: 2(10 −13) +9 = -34 + 60

Step 2: 20 — 26x + 9x = -34x + 60

Step 3: -17x = -34x + 40

Step 4: 17x =40

Step 5: x = 40/17

Realiza los siguientes problemas de Tanto Por Ciento.

1. Se desplaza un camión consumiendo el 60% de su combustible, si el tanque
lleno tiene 45 litros de gasolina ¿Cuántos litros ha consumido?


2. En un gimnasio una persona se pesa y tiene 78 kilogramos de peso, si el peso ideal (100%) para una persona de su edad es de 62 kilogramos ¿Cuales el porcentaje de peso que tiene la persona?

3. Un cohete lunar ha consumido el 20% de su tiempo de vida útil, el cual es de 15 años (100%) ¿Cuânto tiempo de vida útil ha consumido el cohete lunar?

4. El volcán de Pacaya incremento su altitud en 25 metros en su ultima erupción de ceniza, si el volcán mide 2,552 metro ¿Qué porcentaje de altura incremento?

5. Beni tiene el 40% de la edad de su hermano Aarón que tiene 24 años ¿Que edad tiene Beni?

What is the GCF of x^3y^5z^2 and x^4yz^5?
If your are confused the question is also in the picture down below

The expression -7y is a

a. term
b. variable
c. constant

Nathan usually drinks 38 ounces of water per day. He read that he should drink 71 ounces of water per day. If he starts drinking 71 ounces, what is the percent increase?

According to the graph, what is the value of the constant in the equation below?​

Identify the domain and range of the following relation. {(7,-2), (7,4), (7,6), (7,-4), (7,1)