In vertex form, the formula is [tex]f(x) = 2\cdot (x+2)^{2}+1[/tex] and therefore has a minimum value of 1. (Correct choice: A)
In this question we must complete the square and factor the resulting expression to determine coordinates of the vertex:
[tex]f(x) = 2\cdot x^{2}+8\cdot x +9[/tex]
[tex]f(x) = 2\cdot (x^{2}+4\cdot x +4.5)[/tex]
[tex]f(x) = 2\cdot (x^{2}+4\cdot x + 4)+1[/tex]
[tex]f(x) = 2\cdot (x+2)^{2}+1[/tex]
Thus, in vertex form, the formula is [tex]f(x) = 2\cdot (x+2)^{2}+1[/tex] and therefore has a minimum value of 1. (Correct choice: A) [tex]\blacksquare[/tex]
Statement presents typing mistakes and is poorly formatted. Correct form is shown below:
If [tex]f(x) = 2\cdot x ^{2}-8\cdot x +9[/tex], which statement regarding the vertex form of [tex]f(x)[/tex] is true?
A. In vertex form, [tex]f(x) = 2\cdot (x-2)^{2}+1[/tex] and therefore has a minimum value of 1.
B. In vertex form, [tex]f(x) = 2\cdot (x-2)^{2}+1[/tex] and therefore has a minimum value of 2.
C. In vertex form, [tex]f(x) = 2\cdot (x-2)^{2}+4.5[/tex] and therefore has a minimum value of 4.5.
D. In vertex form, [tex]f(x) = 2\cdot (x-2)^{2}+4.5[/tex] and therefore has a minimum value of 2.
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