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When written in vertex form: (h, k) is the vertex of the parabola, and x = h is the axis of symmetry. The graph of g ( x ) = + k translates the graph of f ( x ) = vertically. If k > 0, the graph of f ( x ) = is translated k units up.
equation in vertex form. To determine the vertex from factored form, find the x value that is halfway between the 2 zeros using the mean formula: x= x 1 +x 2 2. To find the y-coordinate, substitute the mean x value into the original equation [ y = a(x – p)(x – q) or y = ax2 + bx + c]. The vertex is (x, y).
Vertex form: ( ) 2 = − + y a x h k. Vertex: (h, k) a > 0 opens up, vertex is a minimum . a < 0 opens down, vertex is a maximum . EXAMPLE: Find the vertex, axis of symmetry, intercepts and graph of . y x 2 =− + + 2( 3) 8 . vertex: axis of symm etry: x-int: y=0 . y-int: x=0
How to Graph a Quadratic Function Given in Vertex Form Graph the function =− t − s2+ u. Quadratic Functions: Vertex Form 1. Identify a, h, and k. • = , ℎ= s, 𝑘= 2. Plot the vertex. • 3. Draw the axis of symmetry. • = s 4. Evaluate the function at two other -values, and plot the points. Use symmetry to plot corresponding points.
To write quadratic functions in vertex form given a graph or situation and to solve situational questions. EX #1: Determine the quadratic function in vertex form for the following graphs.
Quadratic Functions in Vertex Form. For each quadratic function, determine (i) the vertex, (ii) whether the vertex is a maximum or minimum value of the function, (iii) whether the parabola opens upward or downward, (iv) the domain and range, (v) the axis of symmetry, and (vi) on what intervals the graph of the function is increasing and decreasing.
Use the information provided to write the vertex form equation of each parabola. 1) y = x2 + 16 x + 71 y = (x + 8)2 + 7 2) y = x2 − 2x − 5 y = (x − 1)2 − 6 ... 8 Vertex: (2, −4) Axis of Sym.: x = 2 16) f (x) = ...
