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What does it mean when the graph of a quadratic function crosses the x axis twice?
When the graph of a quadratic crosses the x-axis twice it means that the quadratic has two real roots.
If the graph touches the x-axis at one point the quadratic has 1 repeated root.
If the graph does not touch nor cross the x-axis, then the quadratic has no real roots, but it does have 2 complex roots.
What else can I help you with?
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is positive?
It will cross the x-axis twice.
What test is used to determine if a graph is a function?
Horizontal line test is used for the determination of a function,if the horizontal line passes through one point of the given graph then it is a function and if it passes through more than one point then it will not a function. * * * * * No! It is a vertical line test. Consider the graph of y = sin(x): a horizontal line line will cross it twice in every 360 degrees! Convince me that y = sin(x) is not a function.
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
Is signum function differentiable?
The signum function, also known as the sign function, is not differentiable at zero. This is because the derivative of the signum function is not defined at zero due to a sharp corner or discontinuity at that point. In mathematical terms, the signum function has a derivative of zero for all values except at zero, where it is undefined. Therefore, the signum function is not differentiable at zero.
What is 2a equals b?
2a = b Is an example of an equation with linear dependence between the variable a and b (b is twice a)If you know any a you can find the bIf you graph this equation with a on one axis and b on the other (perpendicular) you will get a straight line
When the graph of a quadratic function crosses the x axis twice the x coordinate of the vertex lies between the two x intercepts?
that's true
When the graph of a quadratic function crosses the x-axis twice the x-coordinate of the lies exactly halfway between the two x-intercepts?
Exactly halfway
What does the rule for a quadratic function tell you about how the graph of the function will look?
If the quadratic function is written as ax2 + bx + c then if a > 0 the function is cup shaped and if a < 0 it is cap shaped. (if a = 0 it is not a quadratic) if b2 > 4ac then the equation crosses the x-axis twice. if b2 = 4ac then the equation touches the x-axis (is a tangent to it). if b2 < 4ac then the equation does not cross the x-axis.
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is positive?
It will cross the x-axis twice.
When the graph of a quadratic function crosses the x-axis twice the x-coordinate of the vertex lies between the two x-intercepts?
The x co-ordinate of a quadratic lies exactly halfway between the two x-intercepts, assuming they exist. Alternatively, the x co-ordinate can be found using the formula -B/(2A), when the function is in the form, y = Axx + Bx + C.
How many times will The graph of a quadratic function crosses the x-axis twice?
A quadratic function will cross the x-axis twice, once, or zero times. How often, depends on the discriminant. If you write the equation in the form y = ax2 + bx + c, the so-called discriminant is the expression b2 - 4ac (it appears as part of the solution, when you solve the quadratic equation for "x" - the part under the radical sign). If the discriminant is positive, the x-axis is crossed twice; if it is zero, the x-axis is crossed once, and if the discriminant is negative, the x-axis is not crossed at all.
What is a parabola and quadratic?
A parabola is a line with one curve, that usually crosses the x-axis of a graph twice (unless the roots are imaginary). To find the roots, set y to zero and use the quadratic formula (-b±√b^2-4AC/2A)
When the graph of a quadriatic function crosses the x axis twice the x cordinate of the vertex lies where between the two intercepts?
Precisely midway. That is to say, at their mean (average).
Which type of line that tests for a function?
Vertical line. If you can draw a vertical line through some part of a graph and it will intersect with the graph twice, the graph isn't a function.
How you find the solution of a quadratic equation by graphing its quadratic equation?
When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.
How can you tell if a graph show a FUNCTION?
By doing a vertical line test. If you can draw a vertical line and it only passes through the graph once, its a function. If it passes through twice, it is NOT a function.
Why is the vertical line test used to determine if a graph represents a function?
The definition of a function is "A relation in which exactly one element of the range is paired with each element of the domain." This means that in the relationship of a function, each range element (x value) can only have one domain element (y value). If you draw a vertical line and it crosses your graph twice, then you can see that your x value has two y values, which is not a function.
