Question

Write the equation (in vertex form) of the parabola with the given characteristics:

YOU MUST TYPE f, of, x, equalsf(x)= NOT y, equalsy=

leading coefficient: 33

vertex left parenthesis, 4, comma, 7, right parenthesis(4,7)
Answer
Attempt 1 out of 3

equation:


vertex:


range:

Answer 1

To write the equation of a parabola in vertex form, we use the formula:

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

where \( (h, k) \) is the vertex of the parabola and \( a \) is the leading coefficient.

Given the vertex \( (4, 7) \) and the leading coefficient \( a = 33 \), we can substitute these values into the formula.

Thus, the equation of the parabola is:

\[
f(x) = 33(x - 4)^2 + 7
\]

### Summary:
- **Equation:** \( f(x) = 33(x - 4)^2 + 7 \)
- **Vertex:** \( (4, 7) \)
- **Range:** Since the leading coefficient \( 33 \) is positive, the parabola opens upwards. The minimum value of \( f(x) \) occurs at the vertex \( k = 7 \). Therefore, the range is:

\[
\text{Range: } [7, \infty)
\]

So, your final answer would be:

- **Equation:** \( f(x) = 33(x - 4)^2 + 7 \)
- **Vertex:** \( (4, 7) \)
- **Range:** \( [7, \infty) \)