Question 183833
The y-intercept occurs where {{{x=0}}}, so
{{{y(0) = 2}}} and
{{{y(0) = a*0^2+b*0+c }}}
{{{y(0) = c}}} so,
{{{c = 2}}}
The x-intercepts are the roots
For a quadratic, where {{{y = 0}}}
{{{ax^2+bx+c = 0 }}}
The roots occur at
{{{x = r[1]}}}
{{{x = r[2]}}}
{{{(x - r[1])(x - r[2]) = 0}}} (If {{{x = r[1]}}} or {{{x = r[2]}}}, then
this is true)
given:
{{{r[1] = 1}}}
{{{r[2] = 5}}} so,
{{{(x - 1)(x - 5) = 0}}}
{{{x^2 - 6x + 5 = 0}}}
Multiply both sides by {{{2/5}}}
{{{(2/5)*x^2 - (12/5)*x + 2 = 0}}} answer
I'll plot this
{{{ graph( 500, 500, -10, 10, -10, 10, (2/5)*x^2 - (12/5)*x + 2) }}}