How do you find the curve of a function?

How do you find the curve of a function?

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

Which point is the vertex of the parabola defined by the equation x2 − 6x − 3?

So, the vertex form of y = x2 + 6x – 3 is y = (x+3)2 – 12.

What is the axis of symmetry for the graph of y x2 6x 5?

a=1 , b=−6 , and c=5 . Axis of symmetry: vertical line that separates the parabola into two equal halves, designated x . The axis of symmetry is x=3 .

How do you find the slope of a curve?

For most functions, there is a formula for finding the slope of a curve, f(x), this formula is called the called the derivative (or sometimes the slope formula) and is denoted f/(x). Recall that we already know the slope of a line g(x) = mx + b is this means that the derivative of the line is g/(x) = .

How do you sketch the graph of a parabola?

Sketching Parabolas

1. Find the vertex. We’ll discuss how to find this shortly.
2. Find the y -intercept, (0,f(0)) ( 0 , f ( 0 ) ) .
3. Solve f(x)=0 f ( x ) = 0 to find the x coordinates of the x -intercepts if they exist.
4. Make sure that you’ve got at least one point to either side of the vertex.
5. Sketch the graph.

What is the vertex of y x 2 6x 5?

Here is a graph of y=x2−6x+5 . We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when x=3 and y=−4 . That is the location of the vertex. The coordinate of the vertex is (3,−4) .

How do you find the symmetry of a graph?

Tests for Symmetry

1. A graph will have symmetry about the x -axis if we get an equivalent equation when all the y ‘s are replaced with –y .
2. A graph will have symmetry about the y -axis if we get an equivalent equation when all the x ‘s are replaced with –x .

How to find the shape of a curve using the second derivative?

The second derivative can tell us the shape of a curve at any point. \\displaystyle {x} x. = 2x+3. \\displaystyle> {0} > 0 for all values of x.

How do you find the local minimum of a curve?

\\displaystyle {y}’ y′ changes sign from positive to negative (as we go left to right). Curve showing portion with positive slope in pink, and negative slope in green. A local minimum occurs when y’ = 0 and y’ changes sign from negative to positive.

What are the best tools for sketching functions?

There are now many tools for sketching functions (Mathcad, Scientific Notebook, graphics calculators, etc). It is important in this section to learn the basic shapes of each curve that you meet. An understanding of the nature of each function is important for your future learning. Most mathematical modelling starts with a sketch.