Exercise 151 Page 425

Points where the graph of a function crosses the x-axis are the points where the function reaches 0. It means that we need to find the values of x for which f(x)=0.

(x-2)^2-3 = 0 Note that we obtained a quadratic equation. We can solve it by taking the square roots. To do so, we first need to isolate the expression with the power of 2. Remember to consider the positive and negative solutions.

(x-2)^2-3 = 0

AddEqn

LHS+3=RHS+3

(x-2)^2 = 3

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt((x-2)^2) = sqrt(3)

sqrt(a^2)=± a

x-2=±sqrt(3)

AddEqn

LHS+2=RHS+2

x=± sqrt(3)+2

We found that graph of the given function crosses the x-axis for x=± sqrt(3)+2.

Points where the graph of a function cross the x-axis are the points where the function reaches 0. It means that we need to find the values of x for which f(x)=0.

(x-19)^2(x+14)=0 Note that we obtained a polynomial equation. Since the function is already written in factored form, we will use the Zero Product Property to solve the equation.

(x-19)^2(x+14)=0

ZeroProdProp

Use the Zero Product Property

lc(x-19)^2=0 & (I) x+14=0 & (II)

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(I), (II): Solve for x

SqrtEqn

(I): sqrt(LHS)=sqrt(RHS)

lx-19=0 x+14=0

AddEqn

(I): LHS+19=RHS+19

lx=19 x+14=0