Quadratic functions are used widely in science, business and engineering to model physical phenomena and how quantities change over time. The physical parabolic shape of a quadratic can describe the movement of water in a fountain, the movement of a ball (and in fact any object thrown into the air), or the shape of satellite dishes.
When solving practical problems these steps might be helpful:
When at the solution stage of the problem useful starting points are:
Then we employ one of our solving methods:
Solve the following equation:
$x-\frac{45}{x}=4$x−45x=4
Write all solutions on the same line, separated by commas.
The area of a rectangle is $160$160 square metres. If the length of the rectangle is $6$6 m longer than its width, find the dimensions.
Let $w$w be the width of the rectangle in metres.
First find the width of the rectangle by solving for $w$w.
Now find the rectangle's length.
The product of 2 consecutive, positive numbers is $56$56.
Let the smaller number be $x$x.
Solve for $x$x.
Now find the larger number.
Mae throws a stick vertically upwards. After $t$t seconds its height $h$h metres above the ground is given by the formula $h=25t-5t^2$h=25t−5t2.
At what time(s) will the stick be $30$30 metres above the ground?
The stick takes a total of $T$T seconds to hit the ground. Find the value of $T$T.
Can the stick ever reach a height of $36$36 metres?
Yes
No
The sum of the series 1+2+3+...+$n$n is given by $S$S=$\frac{n\left(n+1\right)}{2}$n(n+1)2.
Find the sum of the first $32$32 integers.
Find the number of integers required for a sum of $15$15. (Let the number of integers be $n$n.)
Solve the following equation for $x$x by substituting in $m=4^x$m=4x.
$4^{2x}-65\times4^x+64=0$42x−65×4x+64=0
Use a comma to separate multiple solutions.