Answer:
y = [tex]\frac{9}{4}[/tex] (x - 2)² - 3
Step-by-step 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 ) = (2, - 3 ) , then
y = a(x - 2)² - 3
To find a substitute (4, 6 ) into the equation
6 = a(4 - 2)² - 3 ( add 3 to both sides )
9 = a(2)² = 4a ( divide both sides by 4 )
[tex]\frac{9}{4}[/tex] = a
y = [tex]\frac{9}{4}[/tex] (x - 2)² - 3 ← in vertex form
