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

Question

Answer 1

Given the vertex (h, k) = (1, 3) and the y-intercept (0, 1), we can use the vertex form of a quadratic function to find the equation.

The vertex form of a quadratic function is:

f(x) = a(x - h)^2 + k

Plug in the vertex (h, k) = (1, 3):

f(x) = a(x - 1)^2 + 3

Now, we'll use the y-intercept point (0, 1) to find the value of 'a'. Plug the x and y values of the y-intercept into the equation:

1 = a(0 - 1)^2 + 3

Solve for 'a':

1 = a(1) + 3

-2 = a

Now that we've found 'a', we can write the equation of the quadratic function in vertex form:

f(x) = -2(x - 1)^2 + 3

The equation of the given quadratic function is:

f(x) = -2(x - 1)^2 + 3

Answer 2

vertex = (1,3)= max point

y=a(x-1)^2 +3

plug in (3,-5) or (-1,-5) to solve for "a"

-5= a(3-1)^2+3= 4a+3

4a=-5-3

a=-8/4=-2

y=-2(x-1)^2 +3

or

y= -2x^2 +4x +1