Chapter 9

If the lead coefficient of \(y=a x^{2}+b x+c\) is a positive number, does the graph of the equation open up or open down?

\(1 x^{2}+15 x+44=0\)

\(x^{2}=81\)

If the lead coefficient of \(y=a x^{2}+b x+c\) is a negative number, does the graph of the equation open up or open down?

\(1 x^{2}+13 x+40=0\)

\(y^{2}=16\)

\(x^{2}+2 x-35=0\)

\(c^{2}=4\)

\(x^{2}+6 x-27=0\)

\(w^{2}=81\)

\(\sqrt{-144}\)

\(p^{2}-27 p+180=0\)

\(y=-x^{2}+3\)

\(\sqrt{-100}\)

\(\sqrt{3^{2}-4(2)(8)}\)

\(2 d^{2}-11 d-40=0\)

\(\sqrt{3^{2}-4(8)(1)}\)

\(x^{2}=169\)

\(\sqrt{3^{2}-4(2)(-8)}\)

\(9 h^{2}-9 h-40=0\)

\(w^{2}=484\)

\(\sqrt{3^{2}-4(8)(-1)}\)

\(9 k^{2}-9 k-28=0\)

\(p^{2}=576\)

\(\sqrt{6^{2}-4(2)(9)}\)

\(25 m^{2}+10 m+1=0\)

\(w^{2}+14 w-32=0\)

\(4 x^{2}=100\)

\(\sqrt{8^{2}-4(4)(8)}\)

\(k^{2}+16 k-17=0\)

\(3 x^{2}=243\)

Explain why the square root of a negative number cannot be a real number.

\(16 u^{2}+24 u+9=0\)

\(w^{2}-14 w-32=0\)

\(\frac{1}{3} x^{2}=50\)

The square root of a negative number is not a real number. However, the cube root of a negative number is a real number. Explain why.

\(36 u^{2}+60 u+25=0\)

\(k^{2}-16 k-17=0\)

\(\frac{1}{2} x^{2}=27\)

\(x^{2}+9 x-11=0\)

\(z^{2}+12 z+11=0\)

\(-x^{2}=-169\)

\(x^{2}+3 x-7=0\)

\(p^{2}+10 p+9=0\)

\(-x^{2}=-196\)

\((5+3 i)+(8+7 i)\)

\(x^{2}-9 x-11=0\)

\(-5 p^{2}=-20\)

\((15+8 i)+(2+4 i)\)

\(x^{2}-3 x-7=0\)