I have tried several times to find the vertex, line of symmetry, max/min value of the quadratic function.
f(x)=-2x+2x+8
I know I have to do completing the square to answer this but everytime i try to follow the steps I stumble hard! a(x-h)^2+k x= -b/2a
x=-2/2(2)=-2/4=-1/2 x+-1/2
for y f(-1/2)
2(-1/2)^2+2(-1/2)+8
That is all i managed and am certain none of it is right either.
Okay I think I have this:
vertex: x=1/2 y=17/2
equation of line of symmetry: x=1/2
Maximum value of f(x)=17/2
Am I correct?
You are correct
Good for you!
Thanks Reiny
To find the vertex, line of symmetry, and maximum/minimum value of a quadratic function, you need to follow a few steps. Let's go through them one by one using your example:
1. Start with the quadratic function: f(x) = -2x^2 + 2x + 8
2. To find the vertex, first identify the values of a, b, and c from the general form of the quadratic equation, ax^2 + bx + c. In this case, a = -2, b = 2, and c = 8.
3. The x-coordinate of the vertex can be found using the formula: x = -b / (2a). Plugging in the values we have, x = -2 / (2 * -2) = 1/2. So, the x-coordinate of the vertex is 1/2.
4. To find the y-coordinate of the vertex, substitute the x-coordinate back into the function: f(1/2) = -2(1/2)^2 + 2(1/2) + 8. Simplifying this expression gives you f(1/2) = -1/2 + 1 + 8 = 17/2. So, the y-coordinate of the vertex is 17/2.
5. The vertex of the quadratic function is the point (1/2, 17/2). This is the maximum or minimum point of the function.
6. The line of symmetry is the vertical line that passes through the vertex. In this case, since the x-coordinate of the vertex is 1/2, the line of symmetry is x = 1/2.
7. Finally, to determine whether the vertex is a maximum or minimum, you can look at the coefficient of the x^2 term. If it is positive, the parabola opens upward and the vertex is a minimum. If it is negative, the parabola opens downward and the vertex is a maximum. In this case, since the coefficient of x^2 is -2 (negative), the parabola opens downward and the vertex (1/2, 17/2) is a maximum.
Remember, completing the square is another method to find the vertex, but in this case, we can use the formula for the x-coordinate of the vertex instead.