Question
Question 3 Simplify the following quadratic equations and rewrite them in standard form. After rewritten, identify the \( a, b \), and \( c \) terms. \( h(t)=-t(16 t+7) \) Standard Form: \( h(t)=\square, b=\square \) \( a=\square \) Question Help: \( D \) Post to forum \( c=\square \) Submit Question
Ask by Mullins Hamilton. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( h(t) = -16t^2 - 7t \), \( a = -16 \), \( b = -7 \), \( c = 0 \).
Solution
1. Expand the given expression:
\[
h(t) = -t(16t + 7) = -16t^2 - 7t
\]
2. Rewrite in standard form \( h(t) = at^2 + bt + c \):
\[
h(t) = -16t^2 - 7t + 0
\]
3. Identify the coefficients:
\[
a = -16,\quad b = -7,\quad c = 0
\]
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Simplify this solution Bonus Knowledge
First, let's simplify the given equation \( h(t) = -t(16t + 7) \). Distributing the \(-t\), we get \( h(t) = -16t^2 - 7t \). This puts the equation in standard form \( h(t) = -16t^2 - 7t + 0 \), making it easy to identify the coefficients: \( a = -16 \), \( b = -7 \), and \( c = 0 \). To ensure clarity, always keep track of the signs while expanding and combining like terms as you simplify equations. One common mistake is forgetting to distribute the negative sign correctly, which can lead to incorrect coefficients. Double-checking your work can save you from unnecessary confusion in later steps!
