Write the equation of the parabola in intercept form (3, 2.25)(4, 0)

Answer 1

y= a(x-h)² +k

h: horizontal shift units --> (x+h)² moves h units left, while (x-h)² moves h units right.

k: vertical shift units, +k: up, -k: down

Since one of the points is at (x,y):(4.0), we know it is one of the x-intercepts, meaning that I will have to form:

y= (ax+C)(x-4)

now, to solve for ax+c, I can replace the data points: (3, 2.25) to get:

2.25 = (3a+C)(3-4)

2.25 = -3a-C

-2.25= C+3a

--> C= -(3a+2.25)

Then we can go back to:

y= (ax+C)(x-4)

y= (ax-3a-2.25)(x-4)

y= ax²-3ax-2.25x+4ax-+12a+9

y= ax²+(a-2.25)x+12a+9

, so at y (@ x=0) = 12a+9

y= (ax+c)(x-4) becomes

12a+9 = (a(0)-3a-2.25)(-4)

12a+9 = 12a+9

a is all real numbers, and because a is conclusive of R,

C also represents all real numbers.

y= (ax+C)(x-4) ; (a,C)€R

This is enough proof to show that what my colleagues mentioned was true about there being infinite solutions. I hope this helps!