Why Can A Function Only Have One Y Intercept?

What is it called when a parabola touches the middle line twice?

Mathematicians call this “turning point” the VERTEX.

We can make the phrase “touches the middle line twice” more formal and more precise by asking: “Does your parabola have two $$ x -intercepts?” Drag the blue points to create a parabola with EXACTLY ONE $$.

What happens if the Y intercept is 0?

If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis. … This slope of this line is undefined. If the line has no x-intercept, then it never intersects the x-axis, so it must be parallel to the x-axis. This means it is a horizontal line, such as .

What to write if there is no Y intercept?

1 Expert Answer If a line never passes through the y axis, therefore having no y intercept, it must be parallel to the y axis, or a vertical line. It is also true that this line is perpendicular to the x axis.

What is the greatest number of y intercepts that a function may have?

If the graph is the graph of a function then it has at most one -intercept, since the graph of a function must pass the vertical line test and the y-axis is one such vertical line. The graph of a function can have any number of -intercepts, including none and infinitely many.

How many y intercepts can a line have?

(Because a function must pass the vertical line test , a function can have at most one y -intercept . ) The y -intercept is often referred to with just the y -value. For example, we say that the y -intercept of the line shown in the graph below is 3.5 .

What does a non zero y intercept mean?

If B is non-zero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis (where x is zero), is CB , and the slope of the line is −AB .

What is the Y intercept in an equation?

Every straight line can be represented by an equation: y = mx + b. … The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

How do you calculate the Y intercept?

You can describe a straight line with the formula y = mx + b, where m is the slope and b is the y-intercept. Now that we know the slope m and a point (x,y), we can use this equation to solve for b, the y-intercept. Fit the slope and point into the equation.

How many y intercepts can the graph of a function have?

If the graph is the graph of a function then it has at most one -intercept, since the graph of a function must pass the vertical line test and the y-axis is one such vertical line. The graph of a function can have any number of -intercepts, including none and infinitely many.

Can a function have no Y-intercept?

In fact, any time a function is undefined at 0, it will have no y-intercept.

Can a parabola have no Y intercept?

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. … The dashed line with each of these parabolas is called the axis of symmetry.

What is the Y intercept in the equation y 4x 3?

the y intercept is always the “b” in a y=mx+b equation. In this equation, the “b” is -3. So -3 is your y intercept.

Is C the Y intercept in a quadratic equation?

The y-intercept of the equation is c. When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.

Where is the Y intercept in a quadratic equation?

The y -intercept is the point at which the parabola crosses the y -axis. 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 .

Can a quadratic function only have one Y-intercept?

The y-intercept is the value at which the graph of the function intersects the y-axis. Every quadratic has a (single) y-intercept. … Thus, the y-intercept of the quadratic function y = ax2 + bx + c is c.