What is the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 )?
1 answer:
Answer:
<u>y = -x² + 4</u>
Step-by-step explanation:
The equation of the parabola in the vertex form is:
y = a (x-h)² + k
Where: (h,k) the coordinates of the vertex & a is a multiplier
The parabola has a vertex at ( 0,4 )
So, h = 0 , k = 4
∴ y = a (x-0)² + 4
∴ y = a x² + 4
The parabola passes through points ( 2,0 )
∴ 0 = a 2² + 4
∴ 4 a = -4 ⇒ a = -4/4 = -1
∴ y = -x² + 4
So, the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 ) is <u>y = -x² + 4</u>
See the attached figure.
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The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
<h3>How to determine the equation?</h3>The attached table of values represents the missing piece in the question.
Start by calculating the rate of change using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (14.77 - 10.55)/(7- 5)
Evaluate
m = 2.11
The equation is then calculated using:
y = m(x - x1) + y1
This gives
y = 2.11(x - 5) + 10.55
Evaluate
y = 2.11x - 10.55 + 10.55
y = 2.11x
Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
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