Calculating y-Values and Roots
Calculate y-values of polynomial functions in Grade 10 by substituting x-values, and find roots by setting the function equal to zero and solving using factoring or the quadratic formula.
Key Concepts
To find a y value for a given x, use the CALC menu's '1: value' feature. To find the x intercept or 'zero' of an equation, use the '2: zero' feature by setting left and right bounds around the intercept.
Find the y value of $y = 3x + 6$ for $x = 2.5$. Using '1: value' gives $y = 13.5$. Find the zero of $y = 4x 12$. Using '2: zero' shows the root is at $x = 3$.
Your graphing calculator is a math whiz! Instead of manually plugging in x values, use the 1: value function for instant answers. To find where your line crosses the x axis (the 'zero'), use the 2: zero feature. It's like a treasure hunt on your graph, guiding you to the exact spot where y equals zero.
Common Questions
How do you find the roots of a polynomial?
Set the polynomial equal to zero and solve. Use factoring, the quadratic formula, or the Rational Root Theorem to identify all x-values where P(x)=0.
How do you evaluate P(x)=x³-4x²+x+6 at x=2?
Substitute: P(2)=8-16+2+6=0. Since P(2)=0, x=2 is a root of the polynomial.
What is synthetic division and when is it used?
Synthetic division is a shorthand method to divide a polynomial by (x-c) and find the remainder. If the remainder is 0, then c is a root. It is faster than long division for linear divisors.