Question

1. A parabola has equation f(x) = Ax^2 + Bx + C. The points P(0,-3), Q(1,7), and R(4, 13) are on this parabola. (i) For each point, write an equation by filling in the x- and f(x)- values. So write three valid equations about this parabola! (ii) Now solve these three equations in three unknowns, to find A, B, and C. (iii) Use (ii) to write the equation of this parabola. (iv) Now, starting from (iii), show all steps of completing the square, to write (iii) in Vertex-form i.e. as f(x) = a(x-h)^2 +k. (v) What is the vertex point of this parabola? And what is the equation of the axis of symmetry? (vi) Calculate all of the x- and y-intercepts of this parabola exactly (i.e. using radicals and fractions), using the form in (iv). DO NOT use the quadratic equation; rather take square roots in (iv). (vii) Graph this parabola (on graph paper). Label the curve with its equation, vertex, axis of symmetry, and intercepts found in (v) and (vi).

          1. A parabola has equation f(x) = Ax^2 + Bx + C. The points
P(0,-3), Q(1,7), and R(4, 13) are on this parabola.

(i) For each point, write an equation by filling in the x- and
f(x)- values. So write three valid equations about this
parabola!

(ii) Now solve these three equations in three unknowns, to
find A, B, and C.

(iii) Use (ii) to write the equation of this parabola.

(iv) Now, starting from (iii), show all steps of completing the
square, to write (iii) in Vertex-form i.e. as
f(x) = a(x-h)^2 +k.

(v) What is the vertex point of this parabola? And what is
the equation of the axis of symmetry?

(vi) Calculate all of the x- and y-intercepts of this parabola
exactly (i.e. using radicals and fractions), using the form
in (iv). DO NOT use the quadratic equation; rather take
square roots in (iv).

(vii) Graph this parabola (on graph paper). Label the curve
with its equation, vertex, axis of symmetry, and
intercepts found in (v) and (vi).

$1. A parabola has equation f(x) = Ax^2 + Bx + C. The points P(0,-3), Q(1,7), and R(4, 13) are on this parabola. (i) For each point, write an equation by filling in the x- and f(x)- values. So write three valid equations about this parabola! (ii) Now solve these three equations in three unknowns, to find A, B, and C. (iii) Use (ii) to write the equation of this parabola. (iv) Now, starting from (iii), show all steps of completing the square, to write (iii) in Vertex-form i.e. as f(x) = a(x-h)^2 +k. (v) What is the vertex point of this parabola? And what is the equation of the axis of symmetry? (vi) Calculate all of the x- and y-intercepts of this parabola exactly (i.e. using radicals and fractions), using the form in (iv). DO NOT use the quadratic equation; rather take square roots in (iv). (vii) Graph this parabola (on graph paper). Label the curve with its equation, vertex, axis of symmetry, and intercepts found in (v) and (vi).$

Added by Adrian V.

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