# Y=4x^{2 -4x+9 find the x-intercepts for the parabola

## Answers

The parabola does not intercept the x-axis.

Step-by-step explanation:

The parabola intercepts the x-axis when [tex]y=0[/tex], then, you need to substitute [tex]y=0[/tex] into the equation:

[tex]y=4x^2 -4x+9\\0=4x^2 -4x+9[/tex]

Now, use the Quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case:

[tex]a=4\\b=-4\\c=9[/tex]

Substituting these values and evaluating, you get:

[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(4)(9)}}{2(4)}\\\\x=\frac{4\±\sqrt{-128}}{8}[/tex]

Remeber that:

[tex]\sqrt{-1}=i[/tex]

Then, rewriting:

[tex]x=\frac{4\±8i\sqrt{2}}{8}[/tex]

Simplifying:

[tex]x=\frac{4(1\±2i\sqrt{2}}{4(2)}\\\\x=\frac{1\±2i\sqrt{2}}{2}\\\\x=\frac{1}{2}\±\frac{2i\sqrt{2}}{2}\\\\x=\frac{1}{2}\±i\sqrt{2}[/tex]

Then:

[tex]x_1=\frac{1}{2}+i\sqrt{2}[/tex]

[tex]x_2=\frac{1}{2}-i\sqrt{2}[/tex]

The roots are complex, therefore, the parabola does not intercept the x-axis.

you can't solve x because it is 2 linear equation and you only have one equation

false

step-by-step explanation:

the meaning of changing is to edit or make something different.

but transmitting means cause (something) to pass on from one place or person to another.

there 2 different things