After transforming f(x) = 2x² +4x + 3 into vertex form, the vertex is easily identifiable. Which ordered pair is the vertex?

Mathematics

1 answer:

jolli1 [7]3 years ago

7 0

The vertex is $(-1,1)$

Explanation:

The equation is $f(x)=2x^{2} +4x+3$

To find the vertex, we need the equation in the form of $f(x)=a (x-h)^{2}+k$

Dividing each term by 2 in the equation $f(x)=2x^{2} +4x+3$

$f(x)=2(x^{2} +2x+\frac{3}{2} )$

Now, completing the square by adding and subtracting 1, we get,

$f(x)=2(x^{2} +2x+1-1+\frac{3}{2} )$

The first three terms can be written as $(x+1)^{2}$ ,

$f(x)=2[(x+1)^{2}+\frac{1}{2} ]$

Multiplying 2 into the bracket, we get,

$f(x)=2(x+1)^{2} +1$

This equation is of the form $f(x)=a (x-h)^{2}+k$

Now, we shall find the vertex $(h,k)$

Thus, $h=-1$ and $k=1$

Thus, the vertex is $(-1,1)$

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ΔCAR has coordinates C (2, 4), A (1, 1), and R (3, 0). A translation maps point C to C' (3, 2). Find the coordinates of A' and R

shutvik [7]

Answer:

$A'= (2,-1)$ and $R'=(4,-2)$ under this translation.

Step-by-step explanation:

A translation in $R^{2}$ is a mapping T from $R^{2}$ to $R^{2}$ defined by $T(x,y) = (x + v_1,y+v_2)$ , where $v=(v_1,v_2)$ is a fixed vector in $R^{2}$ .

From the problem we know that $T(2,4)=(3,2)$ , so we need to find the values $v_1$ and $v_2$ such that $T(2,4) = (2 + v_1,4+v_2)=(3,2)$ , so $3=2 + v_1$ and $4+v_2=2$ , thus $v_1=1$ and $v_2=2$ .