How would I change this problem from standard form to vertex form?
The problem is:
y+6x-16
You typed no equal sign.
If there is to be a vertex, it should be a conic, like a parabola. That means one of the variables must be squared.
Sorry. The equation is y=x+6x-16.
Could you possibly mean
y = (x+6)(x-16) ???
No, that's not what I mean. I am supposed to be changing the equation y= x+6x-16 from standard form to vertex form.
That would lead you to
y = x^2 -10 x - 96
which is indeed a parabola. Since y gets big positive when x gets big positive or negative, it opens up (holds water)
Now complete the square to find the vertex and all
x^2 - 10 x = y + 96
add half of ten squared to both sides, in other words 25
x^2 - 10 x + 25 = y + 121
(x-5)^2 = y+121
vertex at (5 , -121)
well
y= x+6x-16
is a straight line (a line has no vertex)
y = 7 x - 16
in slope intercept form
in standard form like Ax + By = C
that is
7 x - y = 16
Could you mean
y = x^2 + 6 x - 16 ???
that would be
y+16 = x^2 + 6 x
add (6/2)^2 or 9 to both sides
y+25 = x^2 + 6 x + 9
y+25 = (x+3)^2
vertex at ( -3, -25)
i need help with fractions
To change the given problem from standard form to vertex form, we need to complete the square by rewriting it in the form: y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
Let's go step by step:
1. Start with the given equation: y + 6x - 16 = 0
2. Move the constant term (-16) to the right side by adding 16 to both sides:
y + 6x = 16
3. Rearrange the equation by grouping the x and y terms together:
y = -6x + 16
4. To complete the square, focus on the coefficient of x (which is -6). Take half of this coefficient (-6/2 = -3), square it, and add it to both sides of the equation:
y = -6x + 16 --> y = -6x + 9 + 16
Notice that adding 9 to the right side ensures that we maintain the equation's balance.
5. Rearrange and combine like terms on the right side:
y = -6x + 9 + 16 --> y = -6(x - 3)^2 + 25
6. Now, the equation is in vertex form. The vertex is located at (h, k) = (3, 25).
So, the equivalent equation in vertex form is: y = -6(x - 3)^2 + 25