Practice Parameter in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A parameter is a quantity in a mathematical expression that remains constant for a particular case but can change between cases. For example, in y = mx + b, the slope m and intercept b are parameters — each choice of m and b gives a different line.

In y=mx+by = mx + b, mm and bb are parameters — different values give different lines.

Showing a random 20 of 50 problems.

Example 1

medium
In f(x)=asin⁡xf(x) = a \sin x, what role does aa play?

Example 2

easy
In y=mx+5y = mx + 5, which symbol is the variable input?

Example 3

hard
Find aa and bb if the parabola y=ax2+bxy = ax^2 + bx passes through (1,5)(1, 5) and (2,14)(2, 14).

Example 4

medium
For what value of cc does the equation x2−6x+c=0x^2 - 6x + c = 0 have a single (repeated) root?

Example 5

easy
In y=mx+by=mx+b, name the parameters.

Example 6

medium
In the family of parabolas y=(x−h)2y = (x - h)^2, what does the parameter hh control?

Example 7

easy
Are the parameters mm and bb in y=mx+by = mx + b the same for every line, or can they change between lines?

Example 8

medium
The line y=mx+2y=mx+2 passes through (3,8)(3,8). Find the parameter mm.

Example 9

medium
In the family y=mx+by = mx + b, fix b=3b = 3 and vary mm. What do all such lines have in common?

Example 10

medium
In the family y=a(x−2)2+3y = a(x - 2)^2 + 3, find aa if the parabola passes through (4,11)(4, 11).

Example 11

easy
In y=mx+by=mx+b, for one fixed line, does bb stay constant as xx changes?

Example 12

easy
In f(x)=ax2f(x)=ax^2, if aa changes from 1 to 3, does the curve change?

Example 13

easy
In the family y=ax2y = ax^2, what does changing aa do to the graph?

Example 14

medium
Solve for the parameter bb: y=−2x+by = -2x + b passes through (4,1)(4, 1).

Example 15

easy
In y=mx+by=mx+b with m=0m=0, what kind of line results?

Example 16

hard
In the family y=a⋅2xy = a \cdot 2^x, what does the parameter aa represent?

Example 17

easy
In the equation y=3x+by = 3x + b, find bb if the line passes through (0,−4)(0, -4).

Example 18

hard
For what values of kk does the equation x2+kx+4=0x^2 + kx + 4 = 0 have two distinct real roots?

Example 19

easy
In y=mx+7y = mx + 7, what does the parameter mm control?

Example 20

easy
In the quadratic y=ax2+bx+cy = ax^2 + bx + c, how many parameters are there?
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