3 months ago

The graphs below have the same shape. What is the equation of the blue graph?

2 answers:

5 0

Answer: OPTION B

Step-by-step explanation:

The red graph depicts the fundamental form of a quadratic function (the most basic version), with its vertex located at the origin.

The function g(x) results from moving the parent function 2 units to the right and 1 unit upwards.

As a consequence, considering this, the transformation takes the following structure:

$g(x)=(x-h)^2+k$

The horizontal displacement is dictated by the value of h, while the vertical shift is determined by k.

<pThus, the resulting function is:

$g(x)=(x-2)^2+1$

5 0

Answer:

B. $g(x)=(x-2)^2+1$

Step-by-step explanation:

The equation for the red graph is $f(x)=x^2$ .

The blue graph features its vertex at (2,1).

<pTherefore, its equation follows this format:

$g(x)=a(x-2)^2+1$

This graph intersects the y-axis at (0,5).

$5=a(0-2)^2+1$

$5-1=a(-2)^2$

$4=4a$

$1=a$

<pThus, the equation for the blue graph is:

$g(x)=(x-2)^2+1$

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