A translation.
Yes. And the question is ...
That the function is a quadratic expression.
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.
The graph of a quadratic equation is called a parabola.The graph of a quadratic equation is called a parabola.The graph of a quadratic equation is called a parabola.The graph of a quadratic equation is called a parabola.
The slope of your quadratic equation in general form or standard form.
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. And the question is ...
A quadratic function shifts horizontally based on the value of the ( h ) in its vertex form, ( f(x) = a(x - h)^2 + k ). If ( h ) is positive, the graph shifts to the right, while a negative ( h ) causes the graph to shift to the left. This horizontal shift occurs because the input ( x ) is adjusted by subtracting or adding ( h ) from it, changing the location of the vertex along the x-axis.
Some do and some don't. It's possible but not necessary.
The parabola
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 wording is confusing, as a quadratic function is normally a function of one variable. If you mean the graph of y = f(x) where f is a quadratic function, then changes to the variable y will do some of those things. The transformation y --> -y will reflect the graph about the x-axis. The transformation y --> Ay (where A is real number) will cause the graph to stretch or shrink vertically. The transformation y --> y+A will translate it up or down.
Yes.
That the function is a quadratic expression.
A monotonic transformation does not change the overall shape of a function's graph, but it can stretch or compress the graph horizontally or vertically.
When you shift a function, you are essentially translating its graph either horizontally or vertically. A horizontal shift alters the input values, moving the graph left or right, while a vertical shift changes the output values, moving the graph up or down. This transformation maintains the shape of the graph but changes its position in the coordinate plane. Shifting does not affect the function's overall behavior or characteristics, such as its domain and range.