The vertex of the quadratic function y = 2x^2+8x + c is (x, 3)
state the value of x-coordinate of the vertex
state the value of c
help please
the x of the vertex of a quadratic in general form is
-b/(2a)
in this case the x of the vertex is -8/4 = -2
now you know the vertex is (-2,3)
plug that into the equation to find c
so what would "c" be?
To find the x-coordinate of the vertex of the quadratic function, we need to use the formula:
x = -b / (2a)
In this case, the quadratic function is y = 2x^2 + 8x + c. Comparing it to the standard form of a quadratic equation, we can see that a = 2 and b = 8.
Using the vertex coordinates given, (x, 3), we can substitute in 3 for y and solve for x:
3 = 2x^2 + 8x + c
Since the vertex coordinates satisfy this equation, we can substitute 3 for y:
3 = 2x^2 + 8x + c
Now, to find the x-coordinate of the vertex, we'll use the formula:
x = -b / (2a)
Plugging in the values, we get:
x = -8 / (2 * 2)
x = -8 / 4
x = -2
Therefore, the x-coordinate of the vertex is -2.
To find the value of c, we can substitute the x-coordinate of the vertex into the equation:
3 = 2(-2)^2 + 8(-2) + c
3 = 2(4) - 16 + c
3 = 8 - 16 + c
3 = -8 + c
c = 3 + 8
c = 11
Therefore, the value of c is 11.
To find the x-coordinate of the vertex of a quadratic function, we can use the formula `x = -b / (2a)`. In this case, the quadratic function is y = 2x^2 + 8x + c.
Comparing this with the general form of a quadratic function, y = ax^2 + bx + c, we can see that a = 2 and b = 8.
Using the formula for the x-coordinate of the vertex, we can substitute the values a = 2 and b = 8 into the formula:
x = -b / (2a)
x = -8 / (2 * 2)
x = -8 / 4
x = -2
So the x-coordinate of the vertex is -2.
The given information also tells us that the vertex is at (x, 3). This means that when x = -2, the y-coordinate is 3.
Substituting x = -2 into the quadratic function, we can solve for c:
y = 2x^2 + 8x + c
3 = 2(-2)^2 + 8(-2) + c
3 = 8 - 16 + c
3 = -8 + c
c = 3 + 8
c = 11
Therefore, the value of the x-coordinate of the vertex is -2, and the value of c is 11.