What is the equation of the parabola that has a vertex at # (-2, 2) # and passes through point # (3,37) #? Algebra Forms of Linear Equations Write an Equation Given Two Points 1 Answer Vinícius Ferraz Mar 20, 2017 #5y = 7x^2 + 28x + 38# Explanation: #y = ax^2 + bx + c# #V = (-b/(2a), - Delta / (4a)) = (-2, 2)# #b = 4a# #Delta = -8a = (4a)^2 - 4ac Rightarrow a ne 0, c = frac{16a + 8}{4} = 4a + 2# #37 = 9a + 3b + c# #37 = 9a + 12a + 4a + 2# #35 = 25a Rightarrow a = 7/5, b = 28/5, c = 38/5# Answer link Related questions How do you write an equation in slope intercept form given two points? Does it matter which point you use to solve for the y-intercept? What is the formula to find the slope given two points? How do you write the equation for a line containing the points (–4, 1) and (–2, 3)? How do you write the equation for the line containing the points (3, 2) and (–2, 4)? What is the equation in slope intercept form when the slope is undefined? Is it okay for slope to be zero? What is the slope intercept form for a line containing the points (10, 15) and (12, 20)? How do you find the equation of line L that passes through the points (1,3) and (-3,4)? How do you write an equation in slope intercept form for the line through the given point (5,... See all questions in Write an Equation Given Two Points Impact of this question 1077 views around the world You can reuse this answer Creative Commons License