Question

Determine the equation of the graph, and select the correct answer below.

Answer 1

Answer:

The equation of the parabolic function is :

$y=(x-1)^2-3$

Step-by-step explanation:

The standard equation of a parabola is given by:

$y=a(x-h)^2+k$

where $(h,k)$ represents the vertex of the parabola.

From the graph shown in figure we can find the vertex of the parabola which is the minimum point of parabola and lies st point $(1,-3)$

So, we can say:

$(h,k)\rightarrow (1,-3)$

Plugging in the values of vertex in standard equation of parabola,

$y=a(x-1)^2+(-3)$

Simplifying the equation:

$y=a(x-1)^2-3$

We can find value of $a$ by plugging in a point from the graph.

Using point (0,-2) which lies on graph.

Plugging in the given point.

$-2=a(0-1)^2-3$

$-2=a-3$

Adding 3 to both sides.

$-2+3=a-3+3$

$1=a$

∴ $a=1$

Plugging in $a=1$, the equation of parabola can be written as:

$y=(x-1)^2-3$