Question

find the approximate values for which this function cuts the x-axis.
$y = x^2 - 2x - 7$
a ( x = 3.8, x = -1.85 )
b ( x = -3.8, x = 1.85 )
c ( x = -3.8, x = -1.85 )
d ( x = 3.8, x = 1.85 )
e none of these

Explanation:

Step1: Set $y=0$ (x-axis intercept)

$x^2 - 2x - 7 = 0$

Step2: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=1$, $b=-2$, $c=-7$

Step3: Apply quadratic formula

$$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

Step4: Calculate discriminant

$\sqrt{(-2)^2 - 4(1)(-7)} = \sqrt{4 + 28} = \sqrt{32} \approx 5.6568$

Step5: Compute x-values

$x = \frac{2 + 5.6568}{2} \approx 3.828 \approx 3.8$
$x = \frac{2 - 5.6568}{2} \approx -1.828 \approx -1.85$

Answer:

A. $x=3.8, x=-1.85$