Answer:
see explanation
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, 1), thus
y = a(x - 2)² + 1
To find a substitute (0, 7) into the equation
7 = a(0 - 2)² + 1
7 = 4a + 1 ( subtract 1 from both sides )
6 = 4a ( divide both sides by 4 )
a = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{3}{2}[/tex](x - 2)² + 1 ← in vertex form
Expand and simplify
y = [tex]\frac{3}{2}[/tex](x² - 4x + 4) + 1
= [tex]\frac{3}{2}[/tex] x² - 6x + 6x + 1
y = [tex]\frac{3}{2}[/tex] x² - 6x + 7 ← in standard form
