Which of the following must be true in order for two quadratic functions to intersect in an infinite number of locations?
a) They must be the same quadratic function
b) They must share the same vertex, but have different stretch factors
c) The must be reflections of each other around a line
d)They must have different stretch factors and a different vertex
Think about it... Try and make 2 equations that would intersect at an infinite amount of points. Find similarities between the two equations and apply them to this problem.
Rather than think about what is similar between the two, think about what can be different between the two.
They are both quadratic funtions. So they have no holes or anythign like that. They both have the same basic parabolic shape. Can aything about them be different? Are they identical?
My proposition: answer c).
\(f(x)=sin^2(x)\\ g(x)=cos^2(x)\\ axis\ of\ reflection: y=0.5\)
... for two quadratic functions to intersect in an infinite number of locations?
Do quadratic functions have to be parabolas?
There are no parabolas that intersect other parabolas at an infinite number of points.
If they touch at an infinite number of points, they don't intersect.
The function values of f(x) and g(x) are squares between zero and one.
f(x) = sin^2(x) may not fit in the standard expression "quadratic function".
But he fulfills the conditions of the question asked.
If the "quadratic function" is found, please let me know.
Only parabolas are quadratic funtions.
This is the definition of a quadratic function.
A quadratic function is one of the form f(x) = ax^2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. ... A parabola intersects its axis of symmetry at a point called the vertex of the parabola.
An intersection of 2 curves is where the two curves share a common point.
In order for 2 parabolas to share infinitely many points they must effectively be the same parabola.