Table of Contents
- 1 How do you determine if a parabola opens up or down?
- 2 How do you tell if a parabola is stretched or compressed?
- 3 How do you find the vertices of a shifted hyperbola?
- 4 How do you find the pattern of a hyperbola?
- 5 What is the center of a hyperbola with a minus sign?
- 6 What is the standard equation for a hyperbola?
How do you determine if a parabola opens up or down?
There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.
How do you tell if a parabola is stretched or compressed?
If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ) , the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression.
How do you find the vertices of a shifted hyperbola?
The hyperbola is centered at the origin, so the vertices serve as the y-intercepts of the graph. To find the vertices, set x=0 x = 0 , and solve for y y .
How do you know the direction of opening?
If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.
Does the parabola open up or down is the vertex a minimum or a maximum identify the axis of symmetry vertex and the of the parabola?
To find the min/max of a verticle parabola, take the opening of the parabola, either up or down(up in this case). If the parabola opens upward, then the vertex is the min. If the parabola opens downward, then the vertex is the max.
How do you find the pattern of a hyperbola?
There are two patterns for hyperbolas. By examining the equation, we can determine the following: 1. If it is vertical or horizontal. If the x term is positive, the parabola is horizontal (the curves open left and right). If the y term is positive, the parabola is vertical (the curves open up and down).
What is the center of a hyperbola with a minus sign?
Here is the sketch for this hyperbola. In this case the hyperbola will open up and down since the x x term has the minus sign. Now, the center of this hyperbola is ( − 2, 0) ( − 2, 0). Remember that since there is a y 2 term by itself we had to have k = 0 k = 0.
What is the standard equation for a hyperbola?
The standard equation of a hyperbola that we use is ( x – h )^2/ a ^2 – ( y – k )^2/ b ^2 = 1 for hyperbolas that open sideways. If our hyperbola opens up and down, then our standard equation is ( y – k )^2/ a ^2 – ( x – h )^2/ b ^2 = 1.
How do you know if a parabola is vertical or horizontal?
If the x term is positive, the parabola is horizontal (the curves open left and right). If the y term is positive, the parabola is vertical (the curves open up and down). Unlike an ellipse, it does not matter which denominator is larger.