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STU-Kameran Colbart
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What is the vertex of the parabola y equals x2 plus 8x plus 5?
The vertex has a minimum value of (-4, -11)
What is x2 plus 12x equals o?
x2 + 12x = 0 is an equation that describes a parabola. This parabola would have a minimum value and no maximum. That minimum can be found by taking its derivative and solving for zero: y = x2 + 12x dy/dx = x + 12 0 = x + 12 x = -12 Then take that x value and plug it in to the original equation: y = (-12)2 + 12(-12) y = 144 - 144 y = 0 So the focal point of the parabola is at (-12, 0) If you want to factor it, that would come to: x(x + 12) = 0
How can you use the zeros of a function to find the maximum or minimum value of the function?
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
How do you evaluate functions?
To evaluate a function means to replace the variable with some value, and calculate the value of the function. For example, in the parabola y = x2 (or, using functional notation, f(x) = x2), if you replace x with 10, and calculate x2, you are evaluating the function for that specific value.
How do you determine if the graph of a quadratic function has a min or max from its equation?
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
How can you determine the orientation of a parabola when written in standard form?
If the coefficient of x2 is positive then the parabola is cup shaped (happy face). If the coefficient of x2 is negative then the parabola is cap shaped (gloomy face).
What is the y value of the maximum y equals -x2 plus 6x-7?
20 and the vertex of the parabola is at (3, 20)
Determine whether the parabola y equals -x2 plus 15x plus 8 opens up down left or right?
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
What is the equation of a parabola with a vertex at 0 0 and a focus at 0 6?
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
How do you graph a parabola?
y=x2+4x+1
Determine in which direction the parabola opens y equals x2-7x plus 18?
A parabola opens upwards if the quadratic coefficient - the number before the "x2" is positive; downward if it is negative. Note that x2 is the same as 1x2.
What is the standard equation of a parabola?
There are two standard form of parabola: y2 = 4ax & x2 = 4ay, where a is a real number.
