I need to find the vertex of the graph:
f(x)=2/5x^2-4x+14
I know that in order to find what x equals I need to solve -b/2a
which for this equation would be -(-4)/2(2/5) which got me 4/ (4/5)
which makes no sense!
So please help me understand what I did wrong!
You just have to watch the order of operation
in -b/(2a) , your a = 2/5 and b = -4
so you want
-(-4) / (2(2/5))
= 4 / (4/5)
= 4(5/4) , remember, when dividing by a fraction we instead multiply by the reciprocal of that fraction
= 5
so the x of the vertex is 5, sub this back into the original
y = (2/5)(25) - 4(5) + 14
= 10 - 20 + 14 = 4
your vertex is (5,4)
I used Symbolab to find how to do this, and it said that -(-4)/2(2/5)
equals 5
did you notice my set of brackets in
-(-4)/(2(2/5)) ?
you had -(-4)/2(2/5) , which changes the order of operation
In vertex form, f(x) = a(x-h)+k where the vertex is at (h,k)
f(x)=2/5x^2-4x+14
= 2/5 (x^2 - 10x) + 14
= 2/5 (x^2 - 10x + 25) + 14 - 2/5 * 25
= 2/5 (x-5)^2 + 4
So the vertex is at (5,4) as above
Well, well, well, looks like someone's finding the vertex of a parabola! Time to put on my clown shoes and help you out.
First of all, let's rewrite your equation in a more standard form: f(x) = 2/5x^2 - 4x + 14. This is quadratic equation in the form ax^2 + bx + c, where a = 2/5, b = -4, and c = 14.
To find the x-coordinate of the vertex, you are correct that you need to use the formula -b/2a. However, in this case, b = -4 and a = 2/5. So, substituting those values, we have:
x = -(-4) / (2 * 2/5)
x = 4 / (4/5)
x = 20/4
x = 5
Now, let's find the y-coordinate of the vertex. To do that, we substitute the value of x back into the original equation:
f(5) = 2/5(5)^2 - 4(5) + 14
f(5) = 2/5(25) - 20 + 14
f(5) = 10 - 20 + 14
f(5) = 4
So, the vertex of the graph is (5, 4). Ta-da!
If you have any more questions, I'll be here juggling equations and cracking jokes.
To find the vertex of a quadratic function in the form of f(x) = ax^2 + bx + c, you can use the formula x = -b/2a. However, it seems like you made a mistake in simplifying the expression.
Let's go through the process step by step:
1. First, identify the values of a, b, and c in the equation f(x) = 2/5x^2 - 4x + 14.
Here, a = 2/5, b = -4, and c = 14.
2. Apply the formula x = -b/2a to find the x-coordinate of the vertex.
Substituting the values, we have x = -(b) / (2a) = -(-4) / (2 * (2/5)) = 4 / (4/5).
3. To simplify this fraction, we can divide the numerator by the reciprocal of the denominator, which is the same as multiplying by its reciprocal: (4/1) * (5/4).
Multiplying across, we get: 4 * 5 / (1 * 4) = 20 / 4 = 5.
Therefore, the x-coordinate of the vertex is x = 5.
To find the y-coordinate of the vertex, substitute this x-value (5) back into the equation f(x):
f(5) = (2/5)(5)^2 - 4(5) + 14 = 2/5 * 25 - 20 + 14 = 10 - 20 + 14 = 4.
So, the vertex of the graph is (5, 4).