Can a parabola have no x intercepts?

All parabolas are vaguely “U” shaped and they will have a highest or lowest point that is called the vertex. Parabolas may open up or down and may or may not have x -intercepts and they will always have a single y -intercept.

How can a parabola have 2 x intercepts?

If the parabola opens upwards or downwards, and the parabola’s vertex is on the x-axis, then it has one x-intercept. If the parabola opens upwards and the vertex is below the x-axis, or the parabola opens downwards, and the vertex is above the x-axis, then the parabola has two x-intercepts.

Can a graph have 2 x intercepts?

There may be zero, one, or two x -intercepts. These are the same roots that are observable as the x -intercepts of the parabola. Notice that, for parabolas with two x -intercepts, the vertex always falls between the roots.

What are the x intercepts of the parabola?

The x -intercepts are the points at which the parabola crosses the x -axis. If they exist, the x -intercepts represent the zeros, or roots, of the quadratic function, the values of x at which y=0 .

How many X intercepts can a function have?

The graph of a function can have any number of -intercepts, including none and infinitely many. Click to place up to 5 points on the Intercept Graph. A curve will be interpolated through the points and the x- and y-intercepts of that curve will be displayed.

Why do some parabolas not have X intercepts?

If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them.

Can a parabola have 3 x intercepts?

Parabolas can have both x-intercepts and y intercepts A parabola can have either 2,1 or zero real x intercepts.

Does a parabola always have 2 x intercepts?

A parabola can have 2 x-intercepts, 1 x-intercept or zero real x intercepts. If the parabola only has 1 x-intercept (see middle of picture below), then the parabola is said to be tangent to the x-axis.

How many times does a parabola can cross the x-axis?

The graph of a quadratic function is a parabola. A parabola can cross the x-axis once, twice, or never. These points of intersection are called x-intercepts.

How many X intercept can the graph of a quadratic function have how many y intercepts explain your reasoning?

The x-intercept indicates where the parabola graph of that function crosses the x axis. There can be one or two x intercepts for a single quadratic equations. The y-intercept indicates where the parabola crosses the y axis. There is only one y intercept for each quadratic equation.

What is maximum parabola?

Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.

Do all parabolas have two X intercepts?

These are called the intercepts. It is easy to find the y-intercept of a parabola — it always has one — by putting x=0. Not all parabolas, however, have x-intercepts. When x-intercepts exist, they are obtained by putting y=0 and solving the resulting quadratic equation.

https://www.youtube.com/watch?v=UxkNWc9yqvM