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3 years ago

Is this relation a function? Justify your answer.

Mathematics

1 answer:

Alexxandr [17]3 years ago

7 0

Answer:

Yes

Step-by-step explanation:

(I can only read the graph).

Since for each dot, a vertical line drawn through it only intersects that dot, we conclude that the relation is a function.

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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

AnnZ [28]

Answer:

$\textsf{Factored form}: \quad f(x)=2x(x-4)$

$\textsf{Vertex form}: \quad f(x)=2(x-2)^2-8$

Step-by-step explanation:

<u>Factored form of a quadratic function</u>

$f(x)=a(x-p)(x-q)$

where:

p and q are the x-intercepts
a is some constant

Given x-intercepts:

(0, 0)
(4, 0)

Therefore:

$\implies f(x)=a(x-0)(x-4)$

$\implies f(x)=ax(x-4)$

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

$\implies 2a(2-4)=-8$

$\implies -4a=-8$

$\implies a=2$

Therefore, the function's equation in factored form is:

$f(x)=2x(x-4)$

<u>Vertex form of a quadratic equation</u>

<u /> $f(x)=a(x-h)^2+k$

where:

(h, k) is the vertex
a is some constant

Given:

vertex = (2, -8)

Therefore:

$\implies f(x)=a(x-2)^2-8$

To find the constant a, substitute one of the x-intercepts into the equation and solve for a:

$\implies a(0-2)^2-8=0$

$\implies 4a-8=0$

$\implies a=2$

Therefore, the function's equation in vertex form is:

$f(x)=2(x-2)^2-8$

4 0

2 years ago

Read 2 more answers

a recipe calls for 1 tbsp of sugar 2 cups of flour 2 eggs and 4 cups of milk the directions say mix the milk and flour first wri

Pavel [41]

Answer:

4 cups of milk

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

PLZ HELP 13+points iIF U HELP AND ILL MAKE U BRAINLIEST IF RIGHT!!!PLZ and explaine

dedylja [7]

Answer:

A. Picking a red rose from a vase with two red, two pink, two yellow, and two white roses.

Step-by-step explanation:

In this option, there are equal parts of each flower. 2 of each: pink, red, yellow, and white. There is an equal chance (25% [a quarter of one hundred percent]) that you will pick a red, pink, yellow, or white rose.

8 0

3 years ago

g Let P be the plane that goes through the points A(1, 3, 2), B(2, 3, 0), and C(0, 5, 3). Let ` be the line through the point Q(

Sedbober [7]

Answer:

(x, y, z) = (1, 1/3, 3 1/3)

Step-by-step explanation:

The normal to plane ABC can be found as the cross product ...

AB×BC = (1, 0, 2)×(2, -2, -3) = (4, 1, 2)

Then the equation of the plane is ...

4x +y +2z = 4·0 +5 +2·3 . . . . using point C to find the constant

4x +y +2z = 11

The direction vector of the reference line is the vector of coefficients of t: (0, -1, 2). Then the line through point Q is ...

(x, y, z) = (1, 2, 0) +t(0, -1, 2) = (1, 2-t, 2t)

The value of t that puts a point on this line in plane ABC can be found by substituting these values for x, y, and z in the plane's equation.

4(1) +(2 -t) +2(2t) = 11

Solving for t gives ...

t = 5/3

so the point of intersection of the plane and the line is

(x, y, z) = (1, 2-t, 2t) = (1, 2-5/3, 2·5/3) = (1, 1/3, 3 1/3)

5 0

3 years ago

How many lines of symmetry does this have it. If none put 0.

777dan777 [17]

Answer:

<h3>well a line of symmetry is a line that cuts a shape directly in half in this case there is 4 </h3>

Step-by-step explanation:

6 0

3 years ago