Question

Look at the graphs and their equations below. Then fill in the information about the leading coefficients A overline B Cand D

Answer 1

Explanation

,the leading term is the term containing the highest power of x. The coefficient of the leading term is called the leading coefficient.

$\begin{gathered} ax^2+bx+c=0 \\ a\text{ is the leading coefficient} \end{gathered}$

Step 1

a)

an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

therefore

$\begin{gathered} graph\text{ A}\Rightarrow open\text{ downward}\Rightarrow negative \\ graphB\operatorname{\Rightarrow}open\text{upwards}\operatorname{\Rightarrow}pos\imaginaryI t\imaginaryI ve \\ graphC\operatorname{\Rightarrow}\text{ open upwards}\Rightarrow positive \\ graphD\operatorname{\Rightarrow}open\text{downward}\operatorname{\Rightarrow}negat\imaginaryI ve \end{gathered}$

Step 2

b)the leading coefficient "a" indicates how "fat" or how "skinny" the parabola will be.

for

$\begin{gathered} \lvert{leading\text{ coefficent}}\rvert>1,\text{ the parabola will be ''skinny''} \\ \lvert{\text{leadin coefficien}}\rvert$

hence, more the skinny the graph is, the more closet to zero

therefore,the coefficient closest to 0 is C

Step 3

c)simiary, the graph with the leading coefficient with the grates value will be

graph B

because the coefficient is greater than zero and this graph is the more "fat"

I hope this helps you