How do you sketch a graph of a quadratic equation?

How do you sketch a graph of a quadratic equation?

The steps to sketch a quadratic equation by completing the square are:

1. Complete the square. Equation should be in y = a(x – h) 2 + k form (*Memorise)
2. Determine shape and turning point of the curve (*Memorise) If a < 0, it is a maximum curve (‘sad face’)
3. Find the x-intercepts and y-intercept.
4. Plot the graph.

How do you sketch linear equations on a graph?

To graph a linear equation, we can use the slope and y-intercept.

1. Locate the y-intercept on the graph and plot the point.
2. From this point, use the slope to find a second point and plot it.
3. Draw the line that connects the two points.

What is the graph of linear equation called?

The graph of a linear equation in two variables is a line (that’s why they call it linear ). If you know an equation is linear, you can graph it by finding any two solutions.

What does an exponential growth curve show?

Exponential population growth: When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve. In logistic growth, population expansion decreases as resources become scarce. It levels off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.

How do you shift an exponential function?

Shift the graph of f(x)=bx f ( x ) = b x left c units if c is positive and right c units if c is negative. Shift the graph of f(x)=bx f ( x ) = b x up d units if d is positive and down d units if d is negative.

How do you reflect an exponential function?

When we multiply the parent function f(x)=bx f ( x ) = b x by –1, we get a reflection about the x-axis. When we multiply the input by –1, we get a reflection about the y-axis. For example, if we begin by graphing the parent function f(x)=2x f ( x ) = 2 x , we can then graph the two reflections alongside it.

How do you tell if a graph is a polynomial function?

The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will cross the x-axis at zeros with odd multiplicities. The sum of the multiplicities is the degree of the polynomial function.

How can you tell if a graph is a one-to-one function?

An easy way to determine whether a function is a one-to-one function is to use the horizontal line test on the graph of the function. To do this, draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.

How do you tell if a graph has an inverse?

A function f(x) has an inverse, or is one-to-one, if and only if the graph y = f(x) passes the horizontal line test. A graph represents a one-to-one function if and only if it passes both the vertical and the horizontal line tests.

How do you tell if an inverse is a function without graphing?

A way to test if a function is one-to-one is to see if it passes both the vertical and horizontal line test. An example of a one-to-one function is x3. If a function is one-to-one then the function has an inverse.