For what values of a does y = ax2 - 8x +4 have no x-intercepts?

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Note that the graph of  `y=ax^2-8x+4` is a parabola.

A quadratic has no x-intercepts if the discriminant, `b^2-4ac` , is less than 0.

Then `b^2-4ac=(-8)^2-4(a)(4)`

`64-16a<0==>-16a<-64==>a>4` (Note the sign change since we divided by a negative number)


The quadratic `y=ax^2-8x+4` will not have x-intercepts (zeros) if a>4


Graphs of `y=3x^2-8x+4 ("red"),y=4x^2-8x+4("blue"),y=5x^2-8x+4("green")` :