Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,2), vertical axis of symmetry, and contains the point (1,0).
What is (a , b, c)?
+130077 Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,2), vertical axis of symmetry, and contains the point (1,0).
What is (a , b, c)?
In the vertex form, we have
y = a(x - h) + k ⇒ (h , k) = (3,2) .... so.....
0 = a(1 - 3)^2 + 2 subtract 2 from both sides
-2 = a (-2)^2
-2 = 4a divide both sides by 4
-2/4 = a = - 1/2
So we have
y = (-1/2)(x -3)^2 + 2
y = (-1/2)(x^2 - 6x + 9) + 2
y = (-1/2)x^2 + 3x - 9/2 + 2
y = (-1/2)x + 3x - 5/2 ⇒ (a, b, c) = (-1/2, 3, -5/2)
Here's the graph : https://www.desmos.com/calculator/wxrh0uke2u
