Home > Algebra > Quadratic Functions and Their Graphs

How do you write the quadratic function in standard form given points #(-4,-7)#, #(-3,3)#, #(3, -21)#?

Answer 1

Eva Adamson

#y = -2x^2 -4x + 9#

#y = ax^2 + bx + c#

#(-4, -7):# # -7= a(-4)^2 + b(-4) + c# #16a - 4b + c = -7 => eq_1#

#(-3,3):# #3 = a(-3)^2 + b(-3) + c# #9a - 3b + c = 3 => eq_2#

#(3,-21):# #-21 = a(3)^2 + b(3) + c# #9a + 3b + c = -21 => eq_3#

#eq_(1,2&3)# #16a - 4b + c = -7# #9a - 3b + c = 3# #9a + 3b + c = -21# #=> a = -2, b = -4, c = 9#

#y = -2xxx^2 + -4xxx +9# #y = -2x^2 -4x + 9#

https://tutor.hix.ai

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Genesis Allen

To write the quadratic function in standard form given the points (-4, -7), (-3, 3), and (3, -21), you can use the point-slope form to first find the equation, then rewrite it in standard form. Start by using two points to find the slope, then substitute the slope and one point into the point-slope form to get the equation. Finally, rearrange the equation into standard form.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.