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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)

1 answer

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:

  • \( (4, 8) \)
  • \( (5, 8.94) \)
  • \( (0.42, 2.59) \)