Respuesta :
[tex]\begin{gathered} x-\text{intercepts: } \\ x=\text{ 1+ }\frac{2}{\sqrt[]{5}}\text{ or x = 1- }\frac{2}{\sqrt[]{5}} \\ x\text{ = 1.894 or x = 0.106} \end{gathered}[/tex]Explanation:
quadratic function: y = 5(x-1)² - 4
x intercept is gotten when y = 0
representing y with 0 in the quadratic function , we solve for x
0 = 5(x-1)² - 4
collect like terms by adding 4 to both sides:
0+ 4 = 5(x-1)² - 4 + 4
4 = 5(x-1)²
divide both sides by 5:
[tex]\frac{4}{5}=\frac{5\mleft(x-1\mright)^2}{5}[/tex]4/5 = (x-1)²
square root both sides:
[tex]\begin{gathered} \sqrt[]{\frac{4}{5}}=\sqrt[]{(x-1)^2} \\ \pm\sqrt[]{\frac{4}{5}}=\text{ x-1} \end{gathered}[/tex]simplify:
[tex]\begin{gathered} x\text{ - 1 = }\pm\sqrt[]{\frac{4}{5}} \\ x\text{ =1}\pm\text{ }\sqrt[]{\frac{4}{5}}\text{ = 1}\pm\text{ }\frac{\sqrt[]{4}}{\sqrt[]{5}} \\ x\text{ = 1}\pm\text{ }\frac{2}{\sqrt[]{5}} \\ x\text{ = 1+ }\frac{2}{\sqrt[]{5}}\text{ or x = 1- }\frac{2}{\sqrt[]{5}} \\ x\text{ = 1+ 0}.894\text{ or x = 1-0.894} \\ x\text{in tercept: } \\ x\text{ = 1.894 or x = 0.106} \end{gathered}[/tex]