Exercise 14 Page 86

Functions where y varies directly with x^2 — direct variation equations — follow a specific format. y= kx^2 In this form, k≠ 0. By substituting the given values for x and y into the equation, we can determine the constant of variation, k.

y=kx^2

SubstituteII

x= 6, y= 72

72=k( 6)^2

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Solve for k

CalcPow

Calculate power

72=k(36)

RearrangeEqn

Rearrange equation

k(36)=72

DivEqn

.LHS /36.=.RHS /36.

k=72/36

CalcQuot

Calculate quotient

k=2

Now that we have the constant of variation, we can write the function. y= 2x^2 With this equation, we can find any value of x or y when we are given the other. In this case, we are looking for y when x=14.

y=2x^2

Substitute

x= 14

y=2(14)^2

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Solve for y

CalcPow

Calculate power

y=2(196)

Multiply

Multiply

y=392

For the equation y=2x^2, when x=14, the value of y is 392.