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Can you write the equation of a parabola that doesn't cross the x-axis in factored form?
No.
How can a parabola have no x intercepts?
Suppose the equation of the parabola is y = ax2 + bx + c Now, where the parabola crosses the x-axis (the x intercepts), the value of y must be zero (that is what crossing the x-axis means). If the discriminant, b2 - 4ac is less than zero, y has no real roots. This means that there is no real value of x for which y equals zero and so the parabola has no x intercepts. If the discriminant is zero then the parabola only touches the x-axis - at (-b/2a,0). If the discriminant is greater than zero, there are two distinct intercepts. If a>0 then the parabola is shaped like a U and is wholly above the x-axis. If a<0 then the parabola is an upturned U, wholly below the x axis. If a = 0 the quadratic term disappears and the function is a straight line, not a parabola.
How do you get a parabola with only one x intercept?
To have a parabola with only one x-intercept, the vertex of the parabola must lie on the x-axis. This means the parabola opens either upwards or downwards, depending on the coefficient of the squared term in the equation. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By adjusting the coefficients in the equation of the parabola, you can position the vertex such that there is only one x-intercept.
How many times does a porabola cross the x-axis when using imaginary numbers?
NONE If both roots are imaginary, the means the parabola does NOT cross the x-axis at all. The place where a function crosses the x- axis has the coordinate (x,0) for some value of x. That means if you plug in x to the function or polynomial, you get 0. This is equivalent to saying that x is a root of the polynomial. But if the only roots are imaginary, there will be no point (x,0) for any real number x.
How can you tell if a parabola moves up or down in an equation?
Look at the discriminant, B2 - 4AC, in the quadratic equation. As it goes from negative to positive, the parabola moves in the direction of its small end towards the X-axis. At zero, it touches the X-axis.
Can you write the equation of a parabola that doesn't cross the x-axis in factored form?
No.
When does a parabola always cross the x-axis twice?
If the equation of the parabola is represented byy = ax^2 + bx + c then it crosses the x-axis twice if and only if b^2 > 4ac
If the discriminant is negative the graph of a quadratic function will cross or touch the x-axis time s?
If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.
Where do you find the roots when looking at a parabola?
-- The roots of a quadratic equation are the values of 'x' that make y=0 . -- When you graph a quadratic equation, the graph is a parabola. -- The points on the parabola where y=0 are the points where it crosses the x-axis. -- If it doesn't cross the x-axis, then the roots are complex or pure imaginary, and you can't see them on a graph.
Does a parabola always have roots and a vertex?
An x2 parabola will always have one vertex, but depending on the discriminant of the function (b2-4ac) the parabola will either have 2 roots (it crosses the x-axis twice), 1 repeating root (the parabola meets the x-axis at a single point), or no real roots (the parabola doesn't meet the x-axis at all)
What are the zeros of a parabola?
They are the x-values (if any) of the points at which the y-value of the equation representing a parabola is 0. These are the points at which the parabola crosses the x-axis.
How can a parabola have no x intercepts?
Suppose the equation of the parabola is y = ax2 + bx + c Now, where the parabola crosses the x-axis (the x intercepts), the value of y must be zero (that is what crossing the x-axis means). If the discriminant, b2 - 4ac is less than zero, y has no real roots. This means that there is no real value of x for which y equals zero and so the parabola has no x intercepts. If the discriminant is zero then the parabola only touches the x-axis - at (-b/2a,0). If the discriminant is greater than zero, there are two distinct intercepts. If a>0 then the parabola is shaped like a U and is wholly above the x-axis. If a<0 then the parabola is an upturned U, wholly below the x axis. If a = 0 the quadratic term disappears and the function is a straight line, not a parabola.
Was Vanessa White on the x factor?
No... she was at the Y axis... parabola
Is it true graph is reflected about the x-axis and the parabola opens down?
No. A parabola can open up or down.
Where is the line of symmety located on a parabola?
The line of symmetry located on a parabola is right down the center. A parabola is a U shape. Depending on the direction of the parabola it either has a x axis of symmetry or y axis of symmetry. You should have two equal sides of the parabola.
When would not having a parabola x- intercept happen?
Consider a parabola described by the expression y = ax2 + bx + c first, calculate it's first and second derivatives: y' = 2ax + b y'' = 2a Find x value at which y' = 0, and calculate whether the corresponding y-coordinate is above or below the x-axis. If it's above the x-axis, then the parabola will not intercept the x-axis if y'' is greater than 0. If it's below the x-axis, then the parabola will not intercept the x-axis if y'' is less than 0. Otherwise, it will always intercept the x axis at two locations.
How do you get a parabola with only one x intercept?
To have a parabola with only one x-intercept, the vertex of the parabola must lie on the x-axis. This means the parabola opens either upwards or downwards, depending on the coefficient of the squared term in the equation. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By adjusting the coefficients in the equation of the parabola, you can position the vertex such that there is only one x-intercept.
