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How do you find the equation of a parabola in standard form with x intercepts at -2 and 6 passing through 1 and 8?
Since we know the intercepts, its best to solve the general form first and then convert to the standard form.
The intercepts tell us that for some constant, a
y=a*(x+2)(x-6)
We also know that the parabola must run through a given point (1,8) so we can plug that value in to get our value of a
8=a*(3)(-5)
a=-8/15
Next, expand the formula and start moving numbers around until you are in standard form
y=-8/15*(x²-4x-12)
y=-8/15*((x-2)²-16)
y=-8/15*(x-2)²+128/15
What else can I help you with?
What is the graph of a function when it has no gaps or holes?
It is a continuous line whose shape depends upon what expression it is meant to represent.The equation y = x would be a straight line passing through (0,0) and all the other points where the x and y co-ordinates were equal, including negative ones such as (-11,-11).But if the equation has x squared in it the shape would be a parabola, while the graph of an equation with y cubed in it would have something like an S shape in it. More complex equations could produce many differently shaped lines.
What is the solution to the equation y equals -2.5?
The equation y = -2.5 represents a horizontal line on the Cartesian plane passing through the point (-2.5, 0). This line is parallel to the x-axis and has a slope of 0. The solution to this equation is all real numbers on the y-axis that have a value of -2.5.
What is the equation of the axis of symmetry y equals x2 - 8x plus 16?
y = (x-4)(x-4) * * * The factors above are shown correctly. The axis of symmetry is the vertical line passing through the vertex, which is the point located at (4, 0). The equation of that line is x = 4, which is the answer you requested.
What would a graph look like if the equation was x equals 3?
It would look like a straight vertical line, i.e. parallel to the y-axis, passing through the point on the x-axis where x=3.
Graph the equation y equals 2?
Y = 2 The graph is a horizontal line passing through the point Y=2 on the Y=axis. The line is parallel to the X-axis, and exactly 2 units above it everywhere.
How do you find the equation of a parabola in standard form with x intercepts at 0 and 0 passing through 7 and 8?
y = 8/49*x2
What is the parabola equation?
the equation of a parabola is: y = a(x-h)^2 + k *h and k are the x and y intercepts of the vertex respectively * x and y are the coordinates of a known point the curve passes though * solve for a, then plug that a value back into the equation of the parabola with out the coordinates of the known point so the equation of the curve with the vertex at (0,3) passing through the point (9,0) would be.. 0 = a (9-0)^2 + 3 = 0 = a (81) + 3 = -3/81 = a so the equation for the curve would be y = -(3/81)x^2 + 3
Graph this equation 5x plus 10y equals 20?
for the equation:5x + 10y = 20, the two intercepts are:x = 0 , y = 2 or (0,2)y = 0 , x = 4 or (4,0)The graph is a straight line passing through the two intercepts (0,2) and (4,0)
What does the term latus rectum of parabola mean?
The latus rectum of a parabola is a segment with endpoints on the parabola passing through the focus and parallel to the directrix.
Find the equation of line passing through 3 6 and making intercepts equal in magnitude but opposite in sign?
A sample equation could be y = 5/3x + 1, the x-intercept is 1 and the y-intercept is -1.
What's the slope-intercept form of the equation of the line passing through the point -6 3 and parallel to the line y 4 -2?
For a straight line equation to be parallel to another straight line equation they both must have the same slopes but different y intercepts.
Find an equation in standard form for the passing through the points 1 4 and -3 4?
6666
A parabola that opens upward?
A parabola that opens upward is a U-shaped curve where the vertex is the lowest point on the graph. It can be represented by the general equation y = ax^2 + bx + c, where a is a positive number. The axis of symmetry is a vertical line passing through the vertex, and the parabola is symmetric with respect to this line. The focus of the parabola lies on the axis of symmetry and is equidistant from the vertex and the directrix, which is a horizontal line parallel to the x-axis.
What is a term used to describe the relationship between two variables who's graph is a straight line passing through the point 00?
It is a straight line equation with no x or y intercepts on the Cartesian plane
What is the standard for equation of the line passing through the points (3-4) and (51)?
If you mean of points of (3, -4) and (5, 1) then the equation works out as 2y=5x-23
What is the line segment perpendicular to the axis of the parabola and passing through the focus?
It does not have a specific name.
What is the equation of the vertical line passing through (-4-5)?
What is the equation of the vertical line passing through (-5,-2)
