Answer:
y = 2.5x² - 15x + 21.5
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 ) = (3, - 1 ) , then
y = a(x - 3)² - 1
to find a substitute the point (5, 9 ) into the equation
9 = a(5 - 3)² - 1 ( add 1 to both sides )
10 = a(2)² = 4a ( divide both sides by 4 )
= a , then
a = 2.5
the equation of the parabola is then
y = 2.5(x - 3)² - 1 ← expand parenthesis using FOIL
= 2.5(x² - 6x + 9) - 1 ← distribute parenthesis by 2.5
= 2.5x² - 15x + 22.5 - 1
y = 2.5x² - 15x + 21.5 ← equation of parabola