between which two ordered pairs does the graph of $f(x)=\frac{1}{2}x^{2}+x - 9$ cross the negative x…

between which two ordered pairs does the graph of $f(x)=\frac{1}{2}x^{2}+x - 9$ cross the negative x - axis?\nquadratic formula: $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$\n(-6, 0) and (-5, 0)\n(-4, 0) and (-3, 0)\n(-3, 0) and (-2, 0)\n(-2, 0) and (-1, 0)

between which two ordered pairs does the graph of $f(x)=\frac{1}{2}x^{2}+x - 9$ cross the negative x - axis?\nquadratic formula: $x=\frac{-bpmsqrt{b^{2}-4ac}}{2a}$\n(-6, 0) and (-5, 0)\n(-4, 0) and (-3, 0)\n(-3, 0) and (-2, 0)\n(-2, 0) and (-1, 0)

Answer

Explanation:

Step1: Identify coefficients

For $f(x)=\frac{1}{2}x^{2}+x - 9$, $a=\frac{1}{2}$, $b = 1$, $c=-9$.

Step2: Apply quadratic formula

$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-1\pm\sqrt{1^{2}-4\times\frac{1}{2}\times(-9)}}{2\times\frac{1}{2}}=\frac{-1\pm\sqrt{1 + 18}}{1}=-1\pm\sqrt{19}$.

Step3: Find negative root

The negative root is $x=-1-\sqrt{19}$. Since $\sqrt{19}\approx4.36$, then $x=-1 - 4.36=-5.36$.

Answer:

A. $(-6,0)$ and $(-5,0)$