Exercise 147 Page 103

Practice makes perfect

a Examining the equation, we notice that it's written in graphing form. This means we can identify its vertex.

Function:& y=2(x-1)^2+4 Vertex:& (1,4) The parabola has a vertex at (1,4). Also, since the coefficient to the squared term is 2, the function opens upward and is vertically stretched by a factor of 2. Let's calculate a few data points that fall on the graph.

|c|c|c| x & 2(x-1)^2+4 & y -1 & 2( -1-1)^2+4 & 12 0 & 2( 0-1)^2+4 & 6 2 & 2( 2-1)^2+4 & 6 3 & 2( 3-1)^2+4 & 12 By marking the points in a coordinate plane, we can draw the function.

Finally, we will rewrite the equation.

y=2(x-1)^2+4

ExpandNegPerfectSquare

(a-b)^2=a^2-2ab+b^2

y=2(x^2-2(x)(1)+1^2 )+4

▼

Simplify right-hand side

CalcPowProd

Calculate power and product

y=2(x^2-2x+1 )+4

Distr

Distribute 2

y=2x^2-4x+2 +4

AddTerms

Add terms

y=2x^2-4x+6

b The original and rewritten equation are two different ways to write the same function. Therefore, their graphs are identical.

c The equation is a quadratic function. The parent function is therefore the most basic of all quadratic functions.

y=x^2

d From Part B we know that the original and rewritten equation are the same. Therefore, the parent function to the rewritten function is the same as in Part C.

y=x^2