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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.
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.
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.
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
