Question

Which function does the graph represent?

Answer 1

Answer:

The function which represents the graph is:

$y=-\left(x\:-\:2\right)^2+\:3$

Hence, option  B is correct.

The graph is also attached.

Step-by-step explanation:

From the graph, it is clear that:

The vertex = (2, 3)

The y-intercept = (0, -1)

Let us check the equation

$y=-\left(x\:-\:2\right)^2+\:3$

Determining the y-intercept:

The value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

substituting x = 0 in teh equation

$y=-\left(x\:-\:2\right)^2+\:3$

$y=-\left(0\:-\:2\right)^2+\:3$

$y=-2^2+3$

$y=-4+3$

$y=-1$

Thus,

The point representing the y-intercept is:  (0, -1)

Determining the vertex:

The vertex of an up-down facing parabola of the form ax² + bx + c is:

$x_v=-\frac{b}{2a}$

As the equation is

$y=-\left(x\:-\:2\right)^2+\:3$

Rewriting the equation $y=-\left(x\:-\:2\right)^2+\:3$ in the form ax² + bx + c:

$y=-x^2+4x-1$

The Parabola params are:

$a=-1,\:b=4,\:c=-1$

Thus,

$x_v=-\frac{b}{2a}$

$x_v=-\frac{4}{2\left(-1\right)}$

$x_v=2$

Now plug in $x_v=2$ in the equation to find $y_v$

$y_v=-x^2+4x-1$

$\:y_v=-\left(2\right)^2+4\left(2\right)-1$

$y_v=-4+8-1$

$y_v=3$

Therefore, the vertex of the equation is:  (2, 3)

Hence, the function which represents the graph is:

$y=-\left(x\:-\:2\right)^2+\:3$

Hence, option  B is correct.

The graph is also attached.