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2 years ago

9

Which of the following functions best describes this graph?

1 answer:

jok3333 [9.3K]2 years ago

8 0

<h3>Answer: Choice C</h3>

Explanation:

The x intercepts or roots are x = 3 and x = 5, which lead to the factors x-3 and x-5 respectively.

Multiplying out those factors gets us this:

(x-3)(x-5)

x(x-5)-3(x-5)

x^2-5x-3x+15

x^2-8x+15

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

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

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

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

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

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

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

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

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

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

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

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2 years ago

Which statement about the area of a right triangle is true?

timurjin [86]

Answer:

H

Step-by-step explanation:

This is because a rectangle can be divided into two triangles.

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2 years ago

Rewrite the expression with the given base. <br><br> 16^x with a base of 2.

olga55 [171]

Keeping in mind that 16 = 2*2*2*2, thus 16 = 2⁴

$\bf 16^x\implies (2^4)^x\implies 2^{4\cdot x}\implies 2^{4x}$

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2 years ago

Enter the value of 21 + (-3) - (-0.9).<br> PLSS

fomenos

Answer:

18.9

Step-by-step explanation:

21+(-3)-(-0.9) = 21-3+0.9 = 18+0.9 = 18.9

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2 years ago

Test the divisibility of the following :<br>57624 is divisible by 6 ? If It is then explain. <br>

Alisiya [41]

Answer:

yes

Step-by-step explanation:

$57624 \div 6 = 9607$

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2 years ago

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