Question 1085734: Write the equation of a parabola, in standard form, that goes through these points:
(0, 3) (1, 4) (-1, -6)
ax^2 + bx + c = y
a* 0^2+b*0+c=3
a*1^2+b+1+c=4
a*(-1)^2+b(-1)+c= -6
c = 3
a + b + c = 4
a – b + c = -6
a + b + 3 = 4
a – b + 3 = -6
2b = 10
b = 5
A = -4
-4x^2 + 5x + 3 = 0
Graph the parabola above. Indicate the vertex and axis of symmetry.
( i think got the above correct but I'm not as sure about how to graph this type of equation sorry for English)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! You can plot a bunch of points and connect them with a curve (parabola). To make things fast, efficient and error free, you can use technology. A graphing calculator is a great tool. The online graphing calculator given by the link below
https://www.desmos.com/calculator/jculzblpis
The link leads to an interactive graph where you can see that the three blue points are on the red curve. So that graph in the link confirms you have the correct answer. Nice job.
The vertex is (0.625, 4.5625)
The x value of the vertex is found by plugging a = -4 and b = 5 into the formula below
x = -b/(2*a)
Once you know the x coordinate of the vertex, you plug it into the equation y = -4x^2+5x+3 to find the y coordinate of the vertex.
The axis of symmetry is the vertical line x = 0.625, basically the x coordinate of the vertex.
|
|
|
