I have a graph with a parabola on it and asked to write the function for f(x) in standard form.
I know that standard is y=ax^2+bx+c obviously, since the points are on the graph we know x and y so a,b and c need to be found. The vertex is on (4,-4) the points on the left side of the parabola from the vertex up are (3,-3) (2,0) and (1,5). On the right side upwards from the vertex is (5,3) (6,0) and (7,5) I started at the origin to find all the points so if u plot them all and draw te curved lines u will have what I have. Now what do I do???
from the vertex (4,-4)
we can say that parabola must be
y = a(x-4)^2 -4
to find the value of a, let's use one of the other points
e.g. 1,5)
5 = a(-3)^2 - 4
9 = 9a
a = 1
so the parabola is
y = (x-4)^2 -4 or
y = x^2 - 8x + 12
I will leave it up to you to make sure all those other points we did not use are also on this curve by subbing them into our equation.
They should all satisfy the equation,
e.g. I will use (7,5)
LS = 5
RS = 49 - 56 + 12 = 5 = LS
so far so good!
Thanks so much!!!
determine the y-intercept of f(x)=0.2(x-5)^2 - 8, then graph this function on the grid provided. Label any points you plot with the ordered pair.
To determine the y-intercept of the function f(x) = 0.2(x-5)^2 - 8, we can set x = 0 and solve for y.
f(0) = 0.2(0-5)^2 - 8
= 0.2(-5)^2 - 8
= 0.2(25) - 8
= 5 - 8
= -3
So, the y-intercept of the function f(x) is -3.
To graph the function, we can plot additional points and create a smooth curve. Here are a few points we can plot:
When x = 5 (the vertex):
f(5) = 0.2(5-5)^2 - 8
= -8
So, the ordered pair is (5, -8).
When x = 6:
f(6) = 0.2(6-5)^2 - 8
= -7.6
So, the ordered pair is (6, -7.6).
When x = 4:
f(4) = 0.2(4-5)^2 - 8
= -7.8
So, the ordered pair is (4, -7.8).
Now that we have some points, we can plot them on a graph and draw a smooth curve passing through these points. Remember to label the points with their ordered pairs.
To find the function for f(x) in standard form given the vertex and some points on the graph, follow these steps:
1. Start by using the vertex form of a parabola equation, which is f(x) = a(x-h)^2 + k, where (h, k) represents the vertex.
In this case, the vertex is (4, -4), so the equation becomes f(x) = a(x-4)^2 - 4.
2. Now, substitute the x and y values of one of the additional points into the equation to find the value of 'a'.
Let's use the point (3, -3) that lies on the left side of the parabola:
-3 = a(3-4)^2 - 4
-3 = a(-1)^2 - 4
-3 = a - 4
a = 1
3. Substitute the value of 'a' back into the equation of f(x):
f(x) = 1(x-4)^2 - 4
f(x) = (x-4)^2 - 4
Therefore, the function for f(x) in standard form is f(x) = (x-4)^2 - 4.