# Algebra help to find the

**Question description**

**1.
**Consider the parabola f(x) = 3(x-2)^{2}– 1 andthe line *g(x) = 9x -2.*

(i)
**On graph paper **sketch the line and the
parabola. Indicate clearly the vertex of
the parabola, as well as x- or y-intercepts for either. Be sure to use exact
(fractions and radicals) expressions.

(ii) Calculate exactly the two intersection points of the parabola and line, and label them on your sketch. Do this by completing the square.

(iii)
Between
the intersections, the line is above the curve.
Write an equation for *h(x), *the
function giving the **height** of the
line above the curve. Simplify *h(x)* into *ax ^{2 }+ bx + c* form
for your final answer.

(iv)
What
is the DOMAIN of *h(x)?* Answer this
one in a complete sentence.

(v)
Ok,
now complete the square to write your *h(x)*
in the form *A(x-_) ^{2}+B.*

(vi)
*Use *(v)to find the greatest distance between the line and curve.

(vii) Mark this distance with a BAR on your sketch, and label exactly, with coordinates, the top and bottom of the BAR.

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