Question

identify the vertex of the function: y=(x - 2)^2+3. vertex: then convert the quadratic function to standard form. standard form: y=

Explanation:

Step1: Recall vertex - form of quadratic

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For the function $y=(x - 2)^2+3$, $a = 1$, $h = 2$, and $k = 3$. So the vertex is $(2,3)$.

Step2: Expand to standard form

Expand $(x - 2)^2+3$ using the formula $(a - b)^2=a^{2}-2ab + b^{2}$. Here $a=x$ and $b = 2$. So $(x - 2)^2=x^{2}-4x + 4$. Then $y=(x - 2)^2+3=x^{2}-4x+4 + 3=x^{2}-4x + 7$.

Answer:

Vertex: $(2,3)$
Standard Form: $y=x^{2}-4x + 7$