Question

write an equation (any form) for the quadratic graphed below: y =

Explanation:

Step1: Identify vertex form

The vertex - form of a quadratic equation is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. From the graph, the vertex is $(3,0)$, so $h = 3$ and $k = 0$. Then the equation becomes $y=a(x - 3)^2$.

Step2: Find the value of a

We can use another point on the graph, say $(1,4)$. Substitute $x = 1$ and $y = 4$ into $y=a(x - 3)^2$. We get $4=a(1 - 3)^2$. Simplify the right - hand side: $(1 - 3)^2=(-2)^2 = 4$. So $4 = 4a$, and solving for $a$ gives $a = 1$.

Answer:

$y=(x - 3)^2$