Question

1) | If the line of symmetry is x = 1 with the 'a' value from a x? + bx + c = 0 equals 1 pleasegive me a possible equation for this quadratic that satisfies this condition where thex-intercepts are less than 5 units from the stated line of symmetry. Your answer must bejustified for any credit.

Answer 1

line of symmetry is x = 1

a = 1;

`x^2\text{ + bx + c = 0}`

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

`\begin{gathered} x\text{ = }(-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}`

Condition: the x-intercepts are less than5 units from the stated line of symmetry

`\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}`