(0.2,0) is one and I need to find the other using this equation y=5x^2+4x-1?

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Answer 1 · 2018-07-29T16:13:05

Other is $(- 1, 0)$ $(-1,0)$

It appears that you want to find intercepts formed by the parabola on $x$ $x$ -axis.

As on $x$ $x$ -axis, $y = 0$ $y=0$ , we have

$5 x^{2} + 4 x - 1 = 0$ $5x^2+4x-1=0$

or $5 x^{2} + 5 x - x - 1 = 0$ $5x^2+5x-x-1=0$

or $5 x (x + 1) - 1 (x + 1) = 0$ $5x(x+1)-1(x+1)=0$

or $(5 x - 1) (x + 1) = 0$ $(5x-1)(x+1)=0$

Hence either $5 x - 1 = 0$ $5x-1=0$ i.e. $5 x = 1$ $5x=1$ and $x = 0.2$ $x=0.2$

or $x + 1 = 0$ $x+1=0$ i.e. $x = - 1$ $x=-1$

Hence while one intercept is $(0.2, 0)$ $(0.2,0)$ other intercept is $(- 1, 0)$ $(-1,0)$

graph{5x^2+4x-1 [-1.286, 1.214, -1.03, 0.22]}