Answer:
y = [tex]\frac{1}{2}[/tex] x² - x + [tex]\frac{7}{2}[/tex]
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) = (1, 3 ), thus
y = a(x - 1)² + 3
To find a substitute (- 1, 5) into the equation
5 = a(- 1 - 1)² + 3 ( subtract 3 from both sides )
2 = 4a ( divide both sides by 4 )
a = [tex]\frac{1}{2}[/tex] , thus
y = [tex]\frac{1}{2}[/tex] (x - 1)² + 3 ← expand factor using FOIL
y = [tex]\frac{1}{2}[/tex] (x² - 2x + 1) + 3 ← distribute parenthesis
= [tex]\frac{1}{2}[/tex] x² - x + [tex]\frac{1}{2}[/tex] + 3
= [tex]\frac{1}{2}[/tex] x² - x + [tex]\frac{7}{2}[/tex]
