Table of Contents
What makes a graph parabolic?
The graph of a quadratic function is a U-shaped curve called a parabola. The sign on the coefficient a of the quadratic function affects whether the graph opens up or down. If a<0 , the graph makes a frown (opens down) and if a>0 then the graph makes a smile (opens up).
How do you know if a function is parabolic?
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.
What does it mean when a graph is a parabola?
The graph of a quadratic function is a U-shaped curve called a parabola. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.
Why does the graph of a quadratic formula U-shaped parabolic?
The graph of a quadratic function is a U-shaped curve called a parabola. This form allows us to easily find the vertex of the parabola and the axis of symmetry by using the formula for the x-coordinate of the vertex, .
Why is a parabola called a parabola?
The name “parabola” is due to Apollonius, who discovered many properties of conic sections. It means “application”, referring to “application of areas” concept, that has a connection with this curve, as Apollonius had proved. The focus–directrix property of the parabola and other conic sections is due to Pappus.
What is the turning point of the parabola?
The vertex is the turning point of the graph.
Why is a parabola not a function?
If the graph of the parabola does not pass the vertical line test, then that parabola is not a function. A parabola having an equation of the form where is a function. A parabola having an equation of the form is not a function.
Why is vertex of parabola?
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. In this equation, the vertex of the parabola is the point (h,k) . …
What is the U-shaped graph of a quadratic function called?
The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.
How do you tell if a quadratic is U-shaped?
4. The Graph of the Quadratic Function
- If a>0, then the parabola has a minimum point and it opens upwards (U-shaped) eg.
- If a<0, then the parabola has a maximum point and it opens downwards (n-shaped) eg.
- (a) Check if a>0 or a<0 to decide if it is U-shaped or n-shaped.
Why was the parabola invented?
The Greek mathematician Menaechmus (middle fourth century B.C.) is credited with discovering that the parabola is a conic section. He is also credited with using parabolas to solve the problem of finding a geometrical construction for the cubed root of two.