Section 9.1 Day 1 Graphing Quadratic Functions Algebra 1 Section 9.1 Day 1 Graphing Quadratic Functions

Learning Targets Define and identify a quadratic function in standard form Identify a parabola shape and graph which is unique to the quadratic function Define and identify the axis of symmetry, vertex, number of zeros, domain and range of a quadratic graph Identify if the quadratic function has a graph with a maximum or a minimum Graph a quadratic function using a table

Quadratic Function Standard Form: 𝑎 𝑥 2 +𝑏𝑥+𝑐 Example: 2 𝑥 2 +4𝑥−1

Graph of a Quadratic Function Parabola: The shape of a quadratic function (symmetric) Continuous: All points are connected and the graph extends infinitely Smooth Curve: There are no sharp turns or jagged edges Non-Linear: Not a straight line

Axis of Symmetry & Vertex Axis of Symmetry: The vertical line that divides the parabola graph into two symmetrical pieces 𝑥=− 𝑏 2𝑎 Vertex: The lowest or highest point on the parabola graph. This point intersects once with the Axis of Symmetry.

Axis of Symmetry & Vertex 𝑥=− 𝑏 2𝑎 =− 4 2 2 = −1 𝒙=−𝟏 Vertex: (−1, −3)

Number of Zeros Produced The zeros of a function are synonymous with the x- intercepts of a function. A parabola could have one zero, two zeros, or no zeros.

Maximum vs. Minimum Some parabolas will open up and others will open down. Parabolas that open up have a minimum which is the lowest point on the graph. Parabolas that open down have a maximum which is the highest point on the graph.

Domain & Range Domain: All the possible “x-values” that will satisfy a function. Domain is all real numbers Range: All the possible “y-values” produced by the function. Range is 𝑦≥−3

Example 1: Identifying from a Graph Axis of Symmetry: 𝑥=−1 Vertex: (−1, −7) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Minimum Domain: All Real Numbers Range: 𝑦≥−7

Example 2: Identifying from a Graph Axis of Symmetry: 𝑥=2 Vertex: (2,5) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Maximum Domain: All Real Numbers Range: 𝑦≤5

Example 3: Identifying from a Graph Axis of Symmetry: 𝑥=−3 Vertex: (−3, −5) # of Zeros: 2 (x-intercepts) Maximum/Minimum: Minimum Domain: All Real Numbers Range: 𝑦≥−5

Example 4: Identifying from a Graph Axis of Symmetry: 𝑥=1 Vertex: (1, −2) # of Zeros: 0 (x-intercepts) Maximum/Minimum: Maximum Domain: All Real Numbers Range: 𝑦≤−2