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For a quadratic function, there is one minimum/maximum (the proof requires calculus) and also it is either always convex or concave (prove is also calculus) it is continuous every where, hence, it can have a maximum of 2 roots.
Graph it.
If there is more than 2 roots, by Intermediate Value Theorem, it cannot be convex/concave everywhere. It will HAVE to have two intervals of increasing or decreasing. It can be easily proven that given any quadratic function f(x), if x = x0 is a minimum/maximum, and x=a != x0 is a root, then 2x0-a is also a root. It is still true that a = x0 as 2x0-x0=x0 implying it is the only root.
But the concept of min/max requires Calculus to prove existence.
So, this is Calculus, not algebra.
What else can I help you with?
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.
What is the greatest number of x intercepts that a function may have?
The same number as the highest power of the independent variable.
How are solution and x-intercept and zero of a function and and root related?
solutions are the well solution to the problem. X-intercepts are wherever a graph cross the x axis, which are hte solutions when you have to find out what x is, zeros are pretty much the same thing although i think that include y-intercepts as well..... not sure. and roots are the same thing as x-intercepts. so they are all more or less the same thing
Can you solve this using quadratic formula three x squared plus twelve x minus forty-eight?
If you are looking for the zeros of this function: x = -2 plus or minus 2 X the square root of 5.
What is the relationship between the vertex and the x intercepts?
In general, there is no relationship.
What determines if a quadratic function has no x-intercepts?
If the quadratic function is written as ax2 + bx + c, then it has no x-intercepts if the discriminant, (b2 - 4ac), is negative.
Is it possible for the graph of a quadratic function to have two y-intercepts?
Yes. A quadratic function can have 0, 1, or 2 x-intercepts, and 0, 1, or 2 y-intercepts.
Which quadratic function when graphed has x-intercepts of -5 and 2?
(x + 5)(x - 2)x2 + 3x - 10this is your quadratic equation
You can easily identify the x-intercepts of a graph of a quadratic function by writing it as two binomial what?
You can easily identify the x-intercepts of a graph of a quadratic function by writing it as two binomial factors! Source: I am in Algebra 2 Honors!
Does every quadratic function have 2 x intercepts?
Only if the discriminant of its equation is greater than zero will it have 2 different x intercepts.
You can easily identify the x-intercepts of the graph of a quadratic function by writing it as two binomial?
factors
How do you look at a graph and tell what the quadratic function i?
To determine the quadratic function from a graph, first identify the shape of the parabola, which can open upwards or downwards. Look for key features such as the vertex, x-intercepts (roots), and y-intercept. The standard form of a quadratic function is ( f(x) = ax^2 + bx + c ), where ( a ) indicates the direction of the opening. By using the vertex and intercepts, you can derive the coefficients to write the specific equation of the quadratic function.
How do you find the x-intercepts of a quadratic function when it isn't factorisable?
To find the x-intercepts of a quadratic function that isn't factorable, you can use the quadratic formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), where ( ax^2 + bx + c = 0 ) represents the quadratic equation. First, identify the coefficients ( a ), ( b ), and ( c ) from the equation. Then, calculate the discriminant ( b^2 - 4ac ) to determine the nature of the roots. If the discriminant is non-negative, substitute it into the formula to find the x-intercepts.
In the case of a quadratic function what is the number of x and y intercepts the function may have?
The greatest possible number of intercepts is: 2 of one axis and 1 of the other axis.The smallest possible number of intercepts is: One of each axis.
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 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.
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
