Sue Pemberton Solutions for Chapter: Quadratics, Exercise 6: EXERCISE 1F

Find the minimum value of $x^2-7x+8$ and the corresponding value of $x$.

Write $1+x-2x^2$ in the form $p-2(x-q{)}^2$.

Sketch the graph of $y=1+x-2x^2$.

Prove that the graph of $y=4x^2+2x+5$ does not intersect the $x-$axis.

Find the equations of parabolas $A, B$ and $C$.

A parabola passes through the points $(0,-24),(-2,0)$ and $(4,0)$. Find the equation of the parabola.

A parabola passes through the points $(-2,-3),(2,9)$ and $(6,5)$. Find the equation of the parabola.

Prove that any quadratic that has its vertex at $(p, q)$ has an equation of the form $y=a{x}^2-2apx+a{p}^2+q$ for some non-zero real number $a$.