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I assume you meant y2 = 8y + 8x? Subtract 8y: y2 - 8y = 8x. Complete the square: y2 - 8y + 16 = 8x + 16. Extract roots: (y - 4)2 = 8x + 16. Divide by 8: (1/8)(y - 4)2 = x + 2. So the vertex is (-2, 4). To find the focus, first consider the parabola y2/8 = x, which is nothing more than the same parabola, shifted down 4 and leftward 2. To find it's constant distance between focus and directrix, use the equation x = [1/(4p)]y2, and notice that 1/(4p) = 1/8. Solve this equation. Take the reciprocal: 4p = 8. Divide by 4: p = 2. So the distance is 2. It opens to the right, so the focus is 2 to the right of the vertex. The original parabola is the same thing, only translated, so the same thing applies - thus, the focus is 2 to the right of (-2, 4), or (0, 4).
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Find the vertex and equation of the directri for y2 equals -32x?
y2 = 32x y = ±√32x the vertex is (0, 0) and the axis of symmetry is x-axis or y = 0
How do you get a parabola with only one x intercept?
When the vertex lies on the x-axis. For example x = y2, the vertex is at the origin, and the parabola is lying on its side.
What is the expansion for x2 plus y2?
There is no expansion for x2 + y2
What is the result of isolating y2 in the equation below (x plus 4) plus y2 22?
y2=-x2-8x+6
How do you factor 25x2-10xy plus y2?
25x2 - 10xy + y2 = (5x - y)2
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
Find the vertex and equation of the directri for y2 equals -32x?
y2 = 32x y = ±√32x the vertex is (0, 0) and the axis of symmetry is x-axis or y = 0
How do you get a parabola with only one x intercept?
When the vertex lies on the x-axis. For example x = y2, the vertex is at the origin, and the parabola is lying on its side.
What does 4 stands for in equation of parabola square of square of y equals 4ax?
A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right. It's not just the '4' that is important, it's '4a' that matters. This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable. For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)
The parabola defined by y2 equals 4x plus 6?
That would be a horizontal parabola, with it's vertex pointing to the left: y2 = 4x + 6 y2 - 6 = 4x x = y2/4 - 3/2 Now let's find it's vertex, by taking it's derivative and finding the point at which it equals 0: x' = y/2 y = 0 x = 02/4 - 3/2 x = -3/2 So it's vertex occurs at the point (-3/2, 0) Now let's find out where it intercepts the y-axis: x = y2/4 - 3/2 0 = y2/4 - 3/2 y2/4 = 3/2 y2 = 6 y = ±√6 So it intercepts the y-axis at the points (0, -|√6|) and (0, +|√6|)
What is a math function.?
a function in math is most commonly used in graphing and the definition of a function is any equation that when graphed will not have 2 points on the same vertical line. the test for these is known as the vertical line test. functions include parabolas (y=x2, sine curves (y+sin(x)), lines (y=x), and polynomials (x3-4x2+9x) some things that are not functions would be circles (y=y2-x2) or side ways parabolas (x=y2). Ans. A function is a relation in which each element of the 1st set,it corresponds to one and only one element in the 2nd set.
What is Function in maths?
a function in math is most commonly used in graphing and the definition of a function is any equation that when graphed will not have 2 points on the same vertical line. the test for these is known as the vertical line test. functions include parabolas (y=x2, sine curves (y+sin(x)), lines (y=x), and polynomials (x3-4x2+9x) some things that are not functions would be circles (y=y2-x2) or side ways parabolas (x=y2). Ans. A function is a relation in which each element of the 1st set,it corresponds to one and only one element in the 2nd set.
What is y2 plus y2?
y2 + y2 = 2y2
What is a in maths?
a function in math is most commonly used in graphing and the definition of a function is any equation that when graphed will not have 2 points on the same vertical line. the test for these is known as the vertical line test. functions include parabolas (y=x2, sine curves (y+sin(x)), lines (y=x), and polynomials (x3-4x2+9x) some things that are not functions would be circles (y=y2-x2) or side ways parabolas (x=y2). Ans. A function is a relation in which each element of the 1st set,it corresponds to one and only one element in the 2nd set.
How do you get Plato web answer key?
find the x-intercepts of the parabola with vertex (7,-12) and y-intercept (0,135). write your answer in this form:(x1,y1),(x2,y2). if necessary, round to the nearest hundredth.
What is y to the 8th power as an product in four different was with only positive exponents?
y6 x y2 y4 x y4 y2 x y2 x y4 y2 x y2 x y2 x y2
What is y times y?
y2
