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Drawing from Standard Form

Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 2 of 48.

Last time you found the mirror line, x = h. The vertex, the point where the parabola turns, is on that line. Its height is the output at h. So the vertex is (h, f(h)).

For $f\left(x\right) = {x}^{2}+2x-3$ , h = -1 and $f\left(-1\right) = 1 - 2 - 3 = -4$ . So the vertex is (-1, -4). One step to the right, the curve goes up by a. Here a = 1, so the next point is (0, -3). With these two points you can draw the parabola.

$The parabola y = x squared plus 2x minus 3, with its vertex (-1, -4) and the point (0, -3)$

Challenge

Draw $y = {x}^{2}+4x+1$ . Find the vertex first. Then drag the vertex and the second point.

Try it yourself

y = x^{2}+4x+1

Draw the parabola

All lessons in Quadratics & Complex Numbers

1The Vertex

The Axis of SymmetryDrawing from Standard FormMaximum or Minimum Recap: The Vertex

4Imaginary Numbers

Meet i Roots of Negatives Not a Perfect Square Powers of i Recap: Imaginary Numbers

7The Discriminant

Computing It Three Kinds of Answers Reading the Sign Recap: The Discriminant

10Final Challenges

Final: Square It Away Final: The Peak Final: Divide It Final: No Real Roots Final: Where They Meet

2Completing the Square

The Missing Number Completing the Square When a Is Not 1 Recap: Completing the Square

5Complex Arithmetic

Adding and Subtracting Multiplying The Conjugate Dividing A Pure Imaginary Bottom Recap: Complex Arithmetic

8Lines Meet Parabolas

Two Crossings Just Touching No Meeting A Circle and a Line Recap: Lines and Parabolas

3Vertex Form by Algebra

From Standard to Vertex Odd Middle Terms A Leading Number Opening Down Recap: Vertex Form

6Complex Solutions

Squares Equal to Negatives A Shifted Square The Formula Goes Complex Fractions in the Answer Recap: Complex Solutions

9Quadratic Models

The Highest Point Back to the Ground The Biggest Area Price and Revenue Recap: Models