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Does a parabola always have 2 x intercepts?
No, if the vertex of the parabola is (0, 0) it will only have one x intercept. The parabola might have zero x intercepts as well. For example: Y= x^2 + 1 would never touch the x line.
How do you find how many x intercepts the parabola has using the discriminant?
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
What are the zeros of functions and what do they represent?
The zeros of functions are the solutions of the functions when finding where a parabola intercepts the x-axis, hence the other names: roots and x-intercepts.
How do you get the equation of of a parabola from its x-intercepts?
Let us say you X intercepts are -2 and 3 set up (X + 2)(X - 3) FOIL X^2 - X - 6 = 0 ----------------------- your parabolic equation
How do you find the x-intercept of a parabola?
Factorise equation, and look at what x values are needed for the equation to equal zero. Eg. x^2+5x+6 (x+3)(x+2)=0 So parabola intercepts x axis at -3 and -2.
Does a parabola always have 2 x intercepts?
No, if the vertex of the parabola is (0, 0) it will only have one x intercept. The parabola might have zero x intercepts as well. For example: Y= x^2 + 1 would never touch the x line.
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.
What is the vertex of a parabola?
the vertex of a parabola is the 2 x-intercepts times-ed and then divided by two (if there is only 1 x-intercept then that is the vertex)
How do you find how many x intercepts the parabola has using the discriminant?
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
What are the zeros of functions and what do they represent?
The zeros of functions are the solutions of the functions when finding where a parabola intercepts the x-axis, hence the other names: roots and x-intercepts.
How do you get the equation of of a parabola from its x-intercepts?
Let us say you X intercepts are -2 and 3 set up (X + 2)(X - 3) FOIL X^2 - X - 6 = 0 ----------------------- your parabolic equation
What is the parabola?
A parabola is a type of graph that is not linear, and mostly curved. A parabola has the "x squared" sign in it's equation. A parabola is not only curved, but all the symmetrical. The symmetrical point, the middle of the parabola is called the vertex. You can graph this graph with the vertex, x-intercepts and a y-intercept. A parabola that has a positive x squared would be a smile parabola, and the one with the negative x squared would be a frown parabola. Also, there are the parabolas that are not up or down, but sideways Those parabolas have x=y squared, instead of y = x squared.
What are the roots of a parabola?
I think you are talking about the x-intercepts. You can find the zeros of the equation of the parabola y=ax2 +bx+c by setting y equal to 0 and finding the corresponding x values. These will be the "roots" of the parabola.
Why is factoring a useful tool when graphing a parabola?
Factoring will show you where the parabola intercepts the axis.
Where does the parabola x2 plus 8x equals 20 have roots?
x^2+8x=20 x^2+8x-20=0 (x+10)(x-2)=0 x=-10 and x=2 are the roots (intercepts) (-10,0) and (2,0) are the x-intercepts.
How do you find the x-intercept of a parabola?
Factorise equation, and look at what x values are needed for the equation to equal zero. Eg. x^2+5x+6 (x+3)(x+2)=0 So parabola intercepts x axis at -3 and -2.
What are the characteristics of parabolas?
there are three main characteristics of a parabola. these are: 1. vertex: the point at the apex of a parabola 2. x- intercepts: the points at which the parabola intersects or touches the x axis. 3. face: if the parabola is in the form of the letter "u" then it's face is upwards. if the parabola is the in form of the inverted letter "u" then it face downwards :D
