The quadratic equation is y=ax^2 +bx +c. So, you substitute in the values of a, b, and c to the quadratic formula (x= -b +/- \|b^2-4ac all over 2a) in order to find the x value then, substitute in x to the quadratic equation and solve. You will have point (x,y) to graph
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.
The parabola
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
The factors of a quadratic function are expressed in the form ( f(x) = a(x - r_1)(x - r_2) ), where ( r_1 ) and ( r_2 ) are the roots or zeros of the function. These zeros are the values of ( x ) for which the function equals zero, meaning they correspond to the points where the graph of the quadratic intersects the x-axis. Thus, the factors directly indicate the x-intercepts of the quadratic graph, highlighting the relationship between the algebraic and graphical representations of the function.
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
the graph of a quadratic function is a parabola. hope this helps xP
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
Yes it is possible. The solutions for a quadratic equation are the points where the function's graph touch the x-axis. There could be 2 places to that even if the graph looks different.
Yes. And the question is ...
You should always use the vertex and at least two points to graph each quadratic equation. A good choice for two points are the intercepts of the quadratic equation.
The parabola
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
Some do and some don't. It's possible but not necessary.
The factors of a quadratic function are expressed in the form ( f(x) = a(x - r_1)(x - r_2) ), where ( r_1 ) and ( r_2 ) are the roots or zeros of the function. These zeros are the values of ( x ) for which the function equals zero, meaning they correspond to the points where the graph of the quadratic intersects the x-axis. Thus, the factors directly indicate the x-intercepts of the quadratic graph, highlighting the relationship between the algebraic and graphical representations of the function.
Yes.
That the function is a quadratic expression.