Question

Graph the function y = 4 square root of x. Then use the graph to find the missing x- or y-coordinates for the function to the nearest hundredth.

(4,
)

(5,
)

(
, 2.59)

Answer 1

To graph the function \( y = 4\sqrt{x} \), we can calculate a few points by substituting various values of \( x \) into the equation:

1. When \( x = 0 \):
\[
y = 4\sqrt{0} = 0
\]
Point: \( (0, 0) \)

2. When \( x = 1 \):
\[
y = 4\sqrt{1} = 4
\]
Point: \( (1, 4) \)

3. When \( x = 4 \):
\[
y = 4\sqrt{4} = 8
\]
Point: \( (4, 8) \)

4. When \( x = 9 \):
\[
y = 4\sqrt{9} = 12
\]
Point: \( (9, 12) \)

5. When \( x = 16 \):
\[
y = 4\sqrt{16} = 16
\]
Point: \( (16, 16) \)

### Now, we can use this function to find the missing coordinates:

1. For the point \( (4, \_) \):
We already calculated \( y \) when \( x = 4 \):
\[
y = 4\sqrt{4} = 8
\]
So the missing coordinate is \( (4, 8) \).

2. For the point \( (5, \_) \):
We can find \( y \) when \( x = 5 \):
\[
y = 4\sqrt{5} \approx 4 \times 2.236 = 8.944
\]
So the missing coordinate is \( (5, 8.94) \) (rounded to the nearest hundredth).

3. For the point \( (\_, 2.59) \):
We need to find \( x \) when \( y = 2.59 \):
\[
2.59 = 4\sqrt{x}
\]
Divide both sides by 4:
\[
\sqrt{x} = \frac{2.59}{4} \approx 0.6475
\]
Now square both sides to solve for \( x \):
\[
x \approx (0.6475)^2 \approx 0.4192
\]
So, rounding to the nearest hundredth, we have \( (0.42, 2.59) \).

### Final Results:
- \( (4, 8) \)
- \( (5, 8.94) \)
- \( (0.42, 2.59) \)