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.
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.
The same number as the highest power of the independent variable.
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
If you are looking for the zeros of this function: x = -2 plus or minus 2 X the square root of 5.
In general, there is no relationship.
If the quadratic function is written as ax2 + bx + c, then it has no x-intercepts if the discriminant, (b2 - 4ac), is negative.
Yes. A quadratic function can have 0, 1, or 2 x-intercepts, and 0, 1, or 2 y-intercepts.
(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 factors! Source: I am in Algebra 2 Honors!
Only if the discriminant of its equation is greater than zero will it have 2 different x intercepts.
factors
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.
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.
that's true
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.
Exactly halfway
The roots of the quadratic equation are the x-intercepts of the curve.