Spot the Quadratic: Standard Form
Rearrange terms to find a, b, and c in ax² + bx + c = 0.
Equation
y = (2*x^2 - 5) - (x + 1)
Graph
Table
| x | y |
|---|---|
| -3 | 15 |
| -2 | 4 |
| -1 | -3 |
| 0 | -6 |
| 1 | -5 |
| 2 | 0 |
| 3 | 9 |
| 4 | 22 |
What this lesson covers
What you do
You shape the function y = (2*x^2 - 5) - (x + a) and watch the graph answer.
Challenges to clear
- Slide a to 4: the standard form is 2x² − x − 9 = 0. Check f(0) = −9, the constant term.
- Same a: verify f(3) = 6 — coefficients a=2, b=−1, c=−9 all confirmed.
- A steeper quadratic: slide m to 3, so the leading coefficient is 3.
- Now slide a until f(0) reads −11. That constant term is −5 − a, which is what standard form ax² + bx + c makes visible.
Check yourself
In the standard form 2x^2 - x - 9 = 0, what is the value of b?
Why must we rearrange a quadratic equation to equal zero before solving?
- 1 (the coefficient of x on the right)
- -1 (x moves to the left and changes sign) — correct
- -7 (the constant term)
- 0 (there is no bx term on the left initially)
- To make the numbers smaller and easier to calculate.
- To ensure all variables are on the left side.
- Because standard forms like factoring and the quadratic formula require one side to be zero. — correct
- It is just a rule teachers follow, but not strictly necessary.
Think about it
- With a = 4 the equation becomes 2x² − x − 9 = 0. What is the constant term c?