Question

question 22
give the quadratic graphed below
identify the vertex of the parabola
vertex of the parabola is
then write the equation of the parabola in vertex form
y =

Explanation:

Step1: Locate the parabola's vertex

The vertex is the minimum point of the upward-opening parabola, at $(1, 0)$.

Step2: Recall vertex form formula

Vertex form: $y=a(x-h)^2+k$, where $(h,k)$ is vertex.
Substitute $(h,k)=(1,0)$: $y=a(x-1)^2+0 = a(x-1)^2$

Step3: Solve for $a$ using a point

Use the y-intercept $(0,1)$:
$1=a(0-1)^2$
$1=a(1)$
$a=1$

Step4: Write final vertex form

Substitute $a=1$ into the equation.
$y=(x-1)^2$

Answer:

Vertex of the parabola is $(1, 0)$
$y=(x-1)^2$