Find the standard form of the quadratic function shown below:

Question

Quizplus · Accepted Answer

The standard form of a quadratic function is given by $ax^2+bx+c$. By looking at the graph, we can see that the vertex is at $(-2,-3)$ which means that the axis of symmetry is $x=-2$. Therefore, the quadratic function can be written as:
$$a(x+2)^2-3$$
Next, we can use one of the given points on the graph to find the value of $a$. For example, we can use the point $(-4,-7)$:
$$a(-4+2)^2-3=-7 \Rightarrow a(2)^2=4a=4 \Rightarrow a=1$$
Therefore, the quadratic function can be written in standard form as:
$$\boxed{x^2+4x-3}$$

Note: It is important to note that the coefficients of the standard form can be different depending on which point we choose to find the value of $a$. However, only option B has the correct coefficients.

Find the Standard Form of the Quadratic Function Shown Below