b) If 6% of the original amount of C-14 remains, how many years have passed? 13.1 Parabolas and Circles Quadratics often come in (general form) and form “stretched out” “useful” (vertex) Parabolas (vertical) Parabolas (horizontal) General form: y = ax2 + bx + c General: x = ay2 + by + c Vertex form: y = a(x h)2 + k Vertex: x = a(y - k)2 + k – or (y k) = a(x h)2 or (x h) = a(y k)2 – – – – Graphing Procedure (from Chapter 11) Decide direction of opening Find vertex Plot another point to find width Ex a Graph x = - y2 2y + 3 Which way does it face? – Bonus material in videos (skip if you like): Vertex form can be written with the coefficient = , so the vertex forms look like “a” 4p(y k) = (x h)2 (vertical parabola) or – – 4p(x h) = (y k)2 (horizontal parabola) – – The value is significant the distance from the vertex to the focus of the “p” – it’s parabola. Ex 1-bonus: For the equation x2 + 8x = 4y 8, write in standard form. Find – the vertex, focus and graph (see video at https://www.youtube.com/watch?v=CKepZr52G6Y&ab_channel=Mathispower4u
b) If 6% of the original amount of C-14 remains, how many years have passed? 13.1 Parabolas and Circles Quadratics often come in “stretched out” (general form) and “useful” (vertex) form Parabolas (vertical) Parabolas (horizontal) General form: y = ax2 + bx + c General: x = ay2 + by + c Vertex form: y = a(x – h)2 + k Vertex: x = a(y - k)2 + k or (y – k) = a(x – h)2 or (x – h) = a(y – k)2 Graphing Procedure (from Chapter 11) Decide direction of opening Find vertex Plot another point to find width Ex a Graph x = - y2 – 2y + 3 Which way does it face? Bonus material in videos (skip if you like): Vertex form can be written with the coefficient “a” = , so the vertex forms look like 4p(y – k) = (x – h)2 (vertical parabola) or 4p(x – h) = (y – k)2 (horizontal parabola) The value “p” is significant – it’s the distance from the vertex to the focus of the parabola. Ex 1-bonus: For the equation x2 + 8x = 4y – 8, write in standard form. Find the vertex, focus and graph (see video at https://www.youtube.com/watch?v=CKepZr52G6Y&ab_channel=Mathispower4u