Question

Using vertex form, write the equation of the parabola with a vertex at (1,1)
(
1
,
1
)
and a y-intercept at (0,2)
(
0
,
2
)
.(1 point)
The equation in vertex form is

Answer 1

The vertex form of a parabola is given by the equation:

\[
y = a(x - h)^2 + k
\]

where \((h, k)\) is the vertex of the parabola. For your problem, the vertex is \((1, 1)\), so we have:

\[
y = a(x - 1)^2 + 1
\]

Next, we need to find the value of \(a\). We can use the y-intercept, which is given as \((0, 2)\). We substitute \(x = 0\) and \(y = 2\) into the equation:

\[
2 = a(0 - 1)^2 + 1
\]

This simplifies to:

\[
2 = a(1) + 1
\]

\[
2 = a + 1
\]

Subtract 1 from both sides:

\[
a = 1
\]

Now we can substitute \(a\) back into the vertex form equation:

\[
y = 1(x - 1)^2 + 1
\]

This can be simplified to:

\[
y = (x - 1)^2 + 1
\]

Therefore, the equation of the parabola in vertex form is:

\[
\boxed{y = (x - 1)^2 + 1}
\]