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.
No. It can also be a circle, ellipse or hyperbola.
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
Some do and some don't. It's possible but not necessary.
Yes.
That the function is a quadratic expression.
A translation.
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.