Write and equation (any form) for the quadratic graphed below

Question

When I answered the 2/3 tries I am able to do I got f(x)=-1(x-2)^2+3 and the second time i got y=-1x^2+4x-1 and how i got it was -1(x-2) (x-2)+3 i distributed so i got -1(x^2-2x-2x+4)+3 then i combined terms and got -1x^2-4x-4+3 then i got -1x^2-4x-1 as final answer but i got it wrong

Answer 1

1. Find its equation in vertex form y=a(x−h)2+k�=�(�−ℎ)2+�
2. Find its equation in standard form y=ax2+bx+c

Using the vertex of (2,3) and plugging that in as (h,k) into the equation y = a(x - h)² + k

You get y = a(x - 2)² + 3

Then pick another point you know, so let's grab x=0, y=1 and plug that into the above

You get 1 = a(0 - 2)² + 3 and solve for a

a = -2 / (0 - 2)² = -1/2

so: y = -(1 / 2) (x - 2)² + 3 or if you expand the square

y = -(1 / 2) (x² - 4x +4) + 3

y = -½·x²+2·x+1

Answer 2

need (x-2)² since x=2 is vertex,,,,,and when x=2, y=3

have y=a(x-2)²+3

still need to determine a

see x=0, y=1

1=4a+3

a=-(1/2)

Answer 3

The vertex is at (2,3) and the parabola passes through (0,1)--y-intercept.

Using the vertex:

y=A(x-2)²+3

Now use the y-intercept to find A. When x = 0, y = 1.

1=A(-2)²+3

4A=-2

A = -1/2

Equation in vertex form:

y = -1/2 (x-2)²+3

Confirm here:

desmos.com/calculator/ns8r4ikxgx