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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.
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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.
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 the the vertex of a parabola?
The vertex would be the point where both sides of the parabola meet.
Does every line has a y-intercept?
No because a line can be a vertical line so say you have the equation x=5. Then a vertical line would pass through the x intercept 5 and be vertical thus not having a y intercept. All horizontal lines have a y intercept
What form of a quadratic function would be graphed having the vertex at the same point as the y- intercept?
The function would be in the form of ax2+c. The axis of symmetry would be the y-axis, or x = 0, because b would be zero. Likewise, the y-intercept is not important, as any value of c will still yield a vertex at the y-intercept.
How do you use the word intercept in a sentence?
The police intercepted the package before it could be delivered to the suspect's house.
Find the X and Y intercepts of 3x plus 7y equals 42?
The x intercept would be 14 and the y intercept would be 6.
How do you determine the narrowest parabola?
a parabola tht has the highes constant in front of x^2 is the narrowest parabola. let's say u have 2x^2+ 2x-1 and 1/2x^2+2x-1 the narrowest parabola would be the first equation.
How do you work out intercept on a graph?
you put zero in for x and then the answer you get would be the y and then the x,y would be your intercept
What is half of parabola?
A curve. It would be called a parabolic curve.
Purpose of finding the area of a parabola?
If you needed to calculate say, the volume of a gutter, it would be the AREA of the cross-section (parabola) multiplied by the length of the gutter.
Two intercept form in math?
The two intercept forms in math are used mostly in graphing. They would be both x-intercept (or x-intercepts), and y-intercept (or y-intercepts)
