1) The x intercept is the value of x when y is zero
The given equation is expressed as
y = x^2 - 4x - 12
To find the x intercepts, we would make y = 0
Thus, we have
x^2 - 4x - 12 = 0
This is a quadratic equation. The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing,
a = 1, b = - 4, c = - 12
The formula for solving quadratic equations is expressed as
![\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting, } \\ x\text{ = }\frac{-\text{ - 4 }\pm\sqrt[]{-4^2\text{ - 4(1 }*\text{ - 12)}}}{2\text{ }*1} \\ x\text{ = }\frac{4\text{ }\pm\sqrt[]{16\text{ + 48}}}{2} \\ x\text{ = }\frac{4\text{ }\pm\text{ }\sqrt[]{64}}{2} \\ x\text{ = }\frac{4\text{ + 8}}{2}\text{ or x = }\frac{4\text{ - 8}}{2} \\ x\text{ = 6 or x = - 2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/p2exzzt1xczij75aod6ydyw74ynuup2cbi.png)
The x intercepts are x = 6 or x = - 2