The points of intercection between the graph of a quadratic function of the form $ax^{2} +bx+c$ are given by the discriminant of the quadratic formula.

Remember that the quadratic formula is:

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

The discriminant of he quadratic formula is just the thing inside the radical, in other words:

$discriminant=b^{2} -4ac$

- If the discriminant is negative, the graph of the quadratic function doesn't intercept the x-axis.

- If the discriminant is positive, the graph of the quadratic function intercept the x-axis at 2 points.

- If the discriminant is 0, the graph of the quadratic function intercept the x-axis at 1 point.

We can infer form our quadratic that $a=4$ , $b=-9$ , and $c=9$ , so let's replace the values in the discriminant:

$discriminant=b^{2} -4ac$

$discriminant=(-9)^{2} -4(4)(9)$

$discriminant=81-144$

$discriminant=-63$

Since the discriminant is negative, we can conclude that the graph of the quadratic function doesn't intercept the x-axis at any point.

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2 years ago

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Sindrei [870]

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2 years ago