Question

Y=ax^2+bx+c and vertex of the parabola is given (5,8) ; a=4
How many x intercepts does the parabola have?

Answer 1

vertex is given by :
\[(\frac{-b}{2a},\frac{-D}{4a})\],where D is discriminant of quadratic expression.

Answer 2

\[(5,8)=(\frac{-b}{8},\frac{-D}{32})\]
comparing x and y coordinate,
\[\frac{-b}{8}=5\]\[b=-40\]
and
\[\frac{-D}{32}=8\]
\[D=-256\]

Now we know that if :
D>0 , 2 distinct x-intercepts of parabola
D=0 , 2 equal x-intercepts of parabola
D<0 , no x-intercepts of parabola

so here , parabola will have no x-intercepts