y = 2x^2 + x -1
If you know calculus you can find the minimum or maximum when the slope of the equation is zero. This is the first derivative of y with respect to x
dy/dx = 4x +1 = 0
4x = -1
x = -1/4
y = 2 (-1/4)^2 -1/4 -1 = 1/8-1/4-1 = 1/8 - 2/8 - 8/8 = -9/8 minimum = -1.125
The vertex has a minimum value of (-4, -11)
No. By definition, a function has a single unique value for every value passed into it. The equation given here describes a circle, which can not be rearranged to meet this condition.
The function that is given has a constant value and therefore, its slope is 0.
If a + b = 6, what is the value of 3a + 3b?
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
The answer will depend on the ranges for x and y. If the ranges are not restricted, then C can have any value.
The vertex has a minimum value of (-4, -11)
You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.
5 7
No. By definition, a function has a single unique value for every value passed into it. The equation given here describes a circle, which can not be rearranged to meet this condition.
The function that is given has a constant value and therefore, its slope is 0.
y=2x2+5. Plug in 0 for x, and you get y=2(0)^2 +5 =0+5=5. 5 is the minimum value for y.
If a + b = 6, what is the value of 3a + 3b?
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
The function f(x) = 3x + 2 can take any real value, so the question does not seem to make any sense.
It is a quadratic function which represents a parabola.
The minimum value of the parabola is at the point (-1/3, -4/3)