where is the graph?
Can u help me by explaining and show working out 2 this question? I can understand when some1 explains and shows me.....I've attempted it but cant
a) Determine the equation of the function whose graph is shown, given that it has the form y=ax^2 + bx + c, for -6<x<2.
points on graph are; (-6,13) (2,5)
crosses y axis at (0,1)
b) Determine the turning point of the curve.
THIS ISNT FOR AN ASSIGNMENT OR EXAM THING. Just normal work.
Part A.
Use the y-intercept (0,1) to find c.
y = ax^2 + bx + c
1 = a*0 + b * 0 + c
c = 1
Now use one of the other points to find a relation between a and b. I'll use (2,5)
y = ax^2 + bx + 1
5 = a * 2^2 + b * 2 + 1
4 = 4a + 2b
2b = 4 - 4a
b = (4 - 4a)/2
b = 2 - 2a
Now replace b in the original formula with the relation you just found.
y = ax^2 + bx + 1
y = ax^2 + (2 - 2a) * x + 1
Now use that equation and the last point (-6,13) to solve for a.
y = ax^2 + (2 - 2a) * x + 1
13 = a * -6^2 + (2 - 2a) * -6 + 1
13 = a * 36 - 12 + 12a + 1
24 = 36a + 12a
48a = 24
a = 1/2 = 0.5
Now plug a back into the original equation and use any point to find b. I'll use (2,5)
y = ax^2 + bx + 1
y = 0.5 * x^2 + bx + 1
5 = 0.5 * 2^2 + b * 2 + 1
5 = 0.5 * 4 + 2b + 1
2 = 2b
b = 1
Now plug a, b, and c into the original equation
y = ax^2 + bx + c
y = 0.5x^2 + x + 1
Part B
Divide by 0.5
y = 0.5x^2 + x + 1
2y = x^2 + 2x +2
Complete the square
2y = x^2 + 2x + 2
2y = x^2 + 2x + 2 + 1 - 1
2y = x^2 + 2x + 1 + 1
2y = (x + 1)^2 + 1
Divide by 2
2y = (x + 1)^2 + 1
y = 0.5(x + 1)^2 + 0.5
From this equation the x-value at the turning point is -1 and the y-value at the turning point is 0.5. Therefore, (-1,0.5)