Question

Which equation matches the graph shown?please help!

Answer 1

y = - x² + 1

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (0, 1 ) , then

y = a(x - 0)² + 1 = ax² + 1

to find a substitute any other point that lies on the graph into the equation

using (1, 0 ) , then

0 = a(1)² + 1 ( subtract 1 from both sides )

- 1 = a

y = - x² + 1 ← equation of graph

Answer 2

- x² + 1

Explanation:

the vertex of the graph is (0 , 1)

Then the equation of the graph has this form :

(x - 0)² + 1 or - (x - 0)² + 1

Since the parabola is opening down

Then

the equation of the graph is :

- (x - 0)² + 1 = - x² + 1