Question

And I'll scoops or swoops down from its perch and a tree at 20 ft to catch field mice below if I was a function h equals -16 minus 24t + 20 plot the points to the graph the equation which ordered pair represents the vertex

Answer 1

It looks like you have a quadratic function in the form \( h(t) = -16t^2 - 24t + 20 \). To find the vertex of this quadratic equation, we can use the vertex formula for a parabola defined by \( h(t) = at^2 + bt + c \).

The x-coordinate (or t-coordinate) of the vertex is given by the formula:

\[
t = -\frac{b}{2a}
\]

In your equation:

- \( a = -16 \)
- \( b = -24 \)

Substituting these values into the formula:

\[
t = -\frac{-24}{2 \cdot -16} = \frac{24}{-32} = -\frac{3}{4}
\]

Now that we've found \( t = -\frac{3}{4} \), we can find the corresponding \( h(t) \) value (y-coordinate of the vertex) by substituting \( t = -\frac{3}{4} \) back into the function:

\[
h\left(-\frac{3}{4}\right) = -16\left(-\frac{3}{4}\right)^2 - 24\left(-\frac{3}{4}\right) + 20
\]
\[
= -16\left(\frac{9}{16}\right) + 18 + 20
\]
\[
= -9 + 18 + 20
\]
\[
= 29
\]

So, the vertex of the parabola is at \( \left(-\frac{3}{4}, 29\right) \).

**Summary:**
- The ordered pair representing the vertex of the function \( h(t) = -16t^2 - 24t + 20 \) is \( \left(-\frac{3}{4}, 29\right) \).