Our Parabola & Polynomial Goals -- February

Our Parabola & Polynomial Goals -- February Material on Quiz and Exam Student will be able to: • If given Quadratic Function in Standard Form: • ID Vertex, Axis of Symmetry, x and y intercepts • Sketch Parabola • Rewrite equation into Quadratic Fcn‘s Std Form • ID LH and RH Behavior of Polynomials • Perform Long Division of Polynomials • Perform Synthetic Division of Polynomials

Standard Form for a Quadratic Function (Parabola) f(x)=a(x-h)2+k • hAxis of symmetry, its a vertical line at x=h • kVertex at ( h, k ) • … leaving the “a”, which tells us • if the parabola opens upwards or downwards • the “fatness”/ “skinniness” of the parabola

How would we find the x and y intercepts? Substitute O for x (y intercept) and O for y (x intercept) • e.g. f(x)= 3(x-1)2 - 9 • f(x)= 3(0-1)2 - 9 • f(x)= 3( – 1)2 – 9 • f(x)= 3 – 9 • f(x)= – 6 • ( 0, – 6) • y intercept • e.g. f(x)= 3(x-1)2 - 9 • 0= 3(x – 1)2 – 9 • 9=3(x – 1)2 • 9/3=(x – 1)2 • 3=(x – 1)2 • ±√3 = x – 1 • (±√3 +1, 0) • x intercept Can U Graph it?

Sketch it… using h, k and intercepts #s 1 – 8, on page 270 f(x)=5(x-3)2 + 4 f(x)=1(x+3)2 – 4 Then graph these

Let’s do problems in book… page 270, #s 13 – 18,

If we’re given “h” and “k”, and a point on the parabola… We write its function, f(x) • e.g., if h=3, and k=5 and the parabola passes thru (0,0)… f(x)=a(x-h) 2+k • f(x)=a(x-3)2+5 • We can find a by substitution … • 0=a(0-3)2 +5 • –5=9a • – 5/9=a • f(x)= – 5/9(x-3)2+5

What if it is written in the standard form of a quadratic equation… Either rewrite into f(x)=a(x-h)2+kOR Memorize • for ax2+bx+c, memorize: • Vertex is [ –b/2a, f(–b/2a) ] • Axis of symmetry is at x= –b/2a

Our Parabola & Polynomial Goals -- February