# Algebra problem question

**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 *ax2 + 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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