Unit 4, Lesson 9
Standard Form and Factored Form
Integrated Math 2
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Write each quadratic expression in standard form. Draw a diagram if needed.
Consider the expression \(8 - 6x + x^2\).
Which quadratic expression is written in standard form?
\((x+3)x\)
\((x+4)^2\)
\(\text-x^2-5x+7\)
\(x^2+2(x+3)\)
Explain why \(3x^2\) can be said to be in both standard form and factored form.
Jada dropped her sunglasses from a bridge over a river. Which equation could represent the distance, \(y\), fallen in feet, as a function of time, \(t\), in seconds?
\(y=16t^2\)
\(y=48t\)
\(y=180-16t^2\)
\(y=180-48t\)
A football player throws a football. Function \(h\), given by \(h(t)=6+75t-16t^2\) describes the football’s height in feet, \(t\) seconds after it is thrown.
Select all the statements that are true about this situation.
The football is thrown from ground level.
The football is thrown from 6 feet off the ground.
In the function, \(\text-16t^2\) represents the effect of gravity.
The outputs of \(h\) decrease then increase in value.
The function \(h\) has 2 zeros that make sense in this situation.
The vertex of the graph of \(h\) gives the maximum height of the football.
Technology required. Two rocks are launched straight up in the air.
In both functions, \(t\) is time measured in seconds and height is measured in feet. Use graphing technology to graph both equations.