Question

Will the graph of the equation above intersect the x-axis in zero, one, or two points?

Answer 1

Hello!

The answer is:

D. The parabola intercepts the x-axis in two points.

`x_(1)=-0.59\\\\x_(2)=-3.41`

Why?

To find the parabola intercepts, we need to use the quadratic formula. The parabola intercepts with the x-axis, are also called roots or zeroes.

The quadratic formula states that:

`x=\frac{-b+-\sqrt{b^(2)-4ac } }{2a}`

We are given the parabola:

`16x+8=-4x^(2) \\`

Which is also equal to:

`4x^(2)+16x+8=0`

Where,

`a=4\\b=16\\c=8\\`

Then, substituting into the quadratic formula to find the roots of the parabola, we have:

`x=\frac{-b+-\sqrt{b^(2)-4ac } }{2a}\\\\x=\frac{-16+-\sqrt{(16)^(2)-4*4*8 } }{2*4}=(-16+-√((256-128) ) )/(8)\\\\x==(-16+-√((256-128) ) )/(8)=(-16+-√((28 ) )/(8)\\\\x=(-16+-√(128 ) )/(8)=(-16+-(11.31) )/(8)\\\\\\x_(1)=(-16+(11.31) )/(8)=-0.59\\\\x_(1)=(-16-(11.31) )/(8)=-3.41`

Hence,the parabola intercepts the x-axis in two points.

`x_(1)=-0.59\\\\x_(2)=-3.41`

Have a nice day!

Answer 2

Answer: Option D

Explanation:

Add 4x² to both sides of the equation:

`16x+8+4x^2=-4x^2+4x^2\\4x^2+16x+8=0`

The Quadratic formula is:

`x=(-b\±√(b^2-4ac))/(2a)`

You can identify that in this case:

`a=4\\b=16\\c=8`

Substitute into the Quadratic formula:

`x=(-16\±√((16)^2-4(4)(8)))/(2(4))`

`x_1=-0.58\\x_2=-3.41`

Therefore, the graph of the equation above intersect the x-axis in two points.