line of symmetry is x = 1
a = 1;
[tex]x^2\text{ + bx + c = 0}[/tex]Condition: the x-intercepts are less than5 units from the stated line of symmetry
Line of symmetry is given by the formula: x = -b/2a
Remember that x = 1, a = 1
substitute into the formula for the line of symmetry
[tex]\begin{gathered} x\text{ = }\frac{-b}{a}\Rightarrow-b=x\cdot a\Rightarrow\text{ } \\ \text{b = -(x }\cdot\text{ a) = -(1 }\cdot\text{ 1) = -1} \\ b\text{ = -1} \end{gathered}[/tex]Condition: the x-intercepts are less than5 units from the stated line of symmetry
[tex]\begin{gathered} x^2\text{ - x - 2 = 0} \\ (x^{}\text{ - 2}_{})\cdot\text{ (x + 1) = 0} \\ x\text{ - 2 = 0, x + 1 = 0 }\Rightarrow\text{ x = 2, x = -1} \\ We\text{ obtain values of x less than 5 units from the line of symmetry} \end{gathered}[/tex]