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# Which of the following must be true in order for two quadratic functions to intersect in an infinite number of locations?

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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

Jan 25, 2022

#1
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How about you discuss it Julia.  What do YOU think?

Jan 25, 2022
#2
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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.

Jan 25, 2022
#3
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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?

Melody  Jan 25, 2022
edited by Melody  Jan 25, 2022
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"in order for two quadratic functions to intersect in an infinite number of locations"  How can this happen?  One of the curves has to lie exactly on top of the other.  Either curve can be considered the "top" one.

Guest Jan 26, 2022
#4
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Hello Julia!

\(f(x)=sin^2(x)\\ g(x)=cos^2(x)\\ axis\ of\ reflection: y=0.5\)

?

Jan 26, 2022
#5
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This has nothing to do with quadratic functions asinus.

Melody  Jan 26, 2022
#7
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... for two quadratic functions to intersect in an infinite number of locations?

Hello Melody!

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.

!

asinus  Jan 26, 2022
edited by asinus  Jan 26, 2022
edited by asinus  Jan 26, 2022
#8
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Hi asinus,

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.

Melody  Jan 27, 2022