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
(9)
Here (h, k) = (3, - 2), thus
y = a(x - 3)² - 2
To find a substitute (2, 3) into the equation
3 = a(2 - 3)² - 2 ( add 2 to both sides )
5 = a(- 1)² = a , then
y = 5(x - 3)² - 2 ← in vertex form
y = 5(x² - 6x + 9) - 2
= 5x² - 30x + 45 - 2
y = 5x² - 30x + 43 ← in standard form
(10)
Here (h, k) = (2, - 5), thus
y = a(x - 2)² - 5
To find a substitute (5, 4) into the equation
4 = a(5 - 2)² - 5 ( add 5 to both sides )
9 = a(- 3)² = 9a ( divide both sides by 9 )
a = 1
y = (x - 2)² - 5 ← in vertex form
y = x² - 4x + 4 - 5
y = x² - 4x - 1 ← in standard form
