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

Question

asked Mar 12, 2020 229k views

1 Answer

Alessioalex · Answer 1 · 2020-03-17T16:03:22+0000

Answer: The parabola does not intercept the x-axis.

Explanation:

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

$y=4x^2 -4x+9\\0=4x^2 -4x+9$

Now, use the Quadratic formula:

$x=(-b\±√(b^2-4ac))/(2a)$

In this case:

$a=4\\b=-4\\c=9$

Substituting these values and evaluating, you get:

$x=(-(-4)\±√((-4)^2-4(4)(9)))/(2(4))\\\\x=(4\±√(-128))/(8)$

Remeber that:

√(-1)=i

Then, rewriting:

$x=(4\±8i√(2))/(8)$

Simplifying:

$x=(4(1\±2i√(2))/(4(2))\\\\x=(1\±2i√(2))/(2)\\\\x=(1)/(2)\±(2i√(2))/(2)\\\\x=(1)/(2)\±i√(2)$

Then:

x_1=(1)/(2)+i√(2)

x_2=(1)/(2)-i√(2)

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