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How do you find the vertex of the parabola associated with a quadratic equation?
Wiki User
∙ 14y ago
You must first solve the equation for x, find the midpoint between the two x coordinates and substitute it into the equation to find the y coordinate
I.E.
If your equation was y=x^2+4x-5
1. Factorise the Equation and solve for x. x^2+4x-5 = (x+5)(x-1)
So x+5=0
x = 0 - 5
x=-5
And x-1=0
x = 0 + 1
x = 1
So x = -5,1
Find the mid point/average: (-5+1)/2 = -2
So the x coordinate of the vertex is -2.
Substitute this into the equation x^2+4x-5: (-2)^2 + 4*(-2) - 5 = 4 - 8 - 5 = -9
So the Coordinate of the vertex is (-2,-9).
Hope this Helps, message me if you want more info.
Wiki User
∙ 14y ago
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How does finding the vertex of a parabola help you when graphing a quadratic equation?
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
What is the equation of vertex in parabola?
0,0
What is the y-coordinate of the vertex of the parabola that is given by the equation below?
We will be able to identify the answer if we have the equation. We can only check on the coordinates from the given vertex.
Fill in the blank The of the vertex of a quadratic equation is determined by substituting the value of x from the axis of symmetry into the quadratic equation?
D
What is an equation of the parabola in vertex form that passes through (13 8) and has vertex (3 2).?
please help
What different information do you get from vertex form and quadratic equation in standard form?
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
How does finding the vertex of a parabola help you when graphing a quadratic equation?
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
How do you do a parabola?
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
What is the average of the two roots of quadratic equation?
In a quadratic y = ax² + bx + c, the roots are where y = 0, and the parabola crosses the x-axis. The average of these two roots is the x coordinate of the vertex of the parabola.
What is the equation of vertex in parabola?
0,0
The number of solution a quadratic equation has?
A quadratic equation always has 2 solutions.In the instance of perfect squares, however, there will be just one number, which is a double root. Graphically, this is equivalent of the vertex of a parabola just barely touching the x-axis.
What is the equation for vertex form?
The vertex form for a quadratic equation is y=a(x-h)^2+k.
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 are the vertices of the parabolas related to the equation of the quadratic function?
Suppose the equation of the parabola is y = ax2 + bx + c where a, b, and c are constants, and a ≠0. The roots of the parabola are given by x = [-b ± sqrt(D)]/2a where D is the discriminant. Rather than solve explicitly for the coordinates of the vertex, note that the vertical line through the vertex is an axis of symmetry for the parabola. The two roots are symmetrical about x = -b/2a so, whatever the value of D and whether or not the parabola has real roots, the x coordinate of the vertex is -b/2a. It is simplest to substitute this value for x in the equation of the parabola to find the y-coordinate of the vertex, which is c - b2/2a.
What is the maximum or minimum of a quadratic equation called?
The vertex.
What is the equation of a parabola with the vertex of 2 -1?
3
Does a parabola always have roots and a vertex?
Yes, a parabola always has a vertex. However, it may not always have roots. The roots of a parabola are the x-values where the parabola intersects the x-axis. It is possible for a parabola to have two, one, or no roots depending on the discriminant of the quadratic equation.
