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Andre45 [30]
3 years ago
8

What is the equation of a parabola that has a vertex at ( 0,4 ) and passes through points ( 2,0 )?

Mathematics
1 answer:
vlada-n [284]3 years ago
4 0

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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