Cubic Polynomial with degree: 3

QUARTIC Highest exponent is a 4 Polynomial of degree 4

Given: h(x) = 6 x 2 - x – 10 find h(-3) h(-3) = 6 (-3) 2 - (-3) – 10 h(-3) = 6 (9) + 3 – 10 You must square first. h(-3) = 47 This is called evaluating using DIRECT SUBSTITUTION.

Given: h(x) = 6 x 2 - x – 10 find h(-3) We can also evaluate a function using SYNTHETIC SUBSTITUTION. Step 1: We need the coefficients: 6, -1, -10 Step 2: Step 3: Bring down the 6. Multiply it by -3 and then add it to the – Solution

Given: h(x) = 4 x 3 - x – 10 find h(2) Step 1: We need the coefficients: 4, 0, -1, -10 Step 2: Given: h(x) = 4 x 4 - x 2 – 10 We’d have to replace all the “missing” x’s with zeros… h(x) = 4x 4 + 0x 3 – x 2 + 0x - 10

Consider: h(x) = - x 2 - x + 10 What does it graph? What’s it’s y intercept? How could you find it’s x intercepts ? Vertex? Does it flip up or down?

Consider: h(x) = - x 2 - x + 10 It’s called an EVEN function because it is of degree: 2 It’s flips down because the leading coefficient is - 1

Consider: h(x) = 3x 2 - x + 10 It’s called an EVEN function because it is of degree: 2 It’s flips UP because the leading coefficient is 3

Consider: h(x) = - x 3 - x + 10 It’s called an ODD function because it is of degree: 3 It’s flips down because the leading coefficient is - 1

Consider: h(x) = 2x 3 - x + 10 It’s called an ODD function because it is of degree: 3 It’s flips UP because the leading coefficient is 2