Question

Write the equation of a parabola that opens downward with no stretch, given the axis of symmetry is
x
=
3
and the vertex is
(
3
,
11
)
.(1 point)
Responses

y
=
−
(
x
−
3
)
2
−
11
y is equal to negative left parenthesis x minus 3 right parenthesis squared minus 11

y
=
−
(
x
−
3
)
2
+
11
y is equal to negative left parenthesis x minus 3 right parenthesis squared plus 11

y
=
−
(
x
+
3
)
2
+
11
y is equal to negative left parenthesis x plus 3 right parenthesis squared plus 11

y
=
−
(
x
+
11
)
2
−
3

Answer 1

To write the equation of a parabola that opens downward, we can use the vertex form of a parabola, which is:

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

where \((h, k)\) is the vertex of the parabola. In this case, the vertex is given as \((3, 11)\), so \(h = 3\) and \(k = 11\). Since the parabola opens downward, \(a\) will be negative. Given that there's no stretch, we can assume \(a = -1\).

Plugging in the values into the vertex form, we get:

\[
y = -1(x - 3)^2 + 11
\]

This simplifies to:

\[
y = -(x - 3)^2 + 11
\]

Therefore, the correct equation of the parabola is:

**y = -(x - 3)^2 + 11**

So, the corresponding response is:

**y = −(x − 3)^2 + 11**.