# Identify the vertex of each graph; identify whether it is a...

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PULLO Notes on Quadratic Functions A QUADRATIC EQUATION is a function that can be written in the form 2 y ax bx c where a, b, and c are real numbers and a 0. Examples: 2 5 y x 2 2 7 y x  2 3 y x x The graph of a quadratic function is a U-shaped curve called a PARABOLA . The maximum or minimum point is called the VERTEX. Identify the vertex of each graph; identify whether it is a minimum or a maximum. 1.) 2.) Vertex: ( , ) _________ Vertex: ( , ) _________ x x . y. What is the direction of opening? _______
Is the vertex a max or min? _______ Fatter or thinner than y = x 2 ? __________ (A STRETCH OR SHRINK) Is the vertex a max or min? _______ Wider or narrower than y = x 2 ? ___________ (A STRETCH OR SHRINK) Y = X 2 THE PARENT GRAPH The parabola y = x 2 is graphed to the right. Note its vertex (0,0) and its width. You will be asked to compare other parabolas to this graph. Graphing in STANDARD FORM ( 2 y ax bx c ): we need to find the vertex 1st Vertex - List a = ____, b = ____, c = ____ - Find x = 2 b a - Plug this x -value into the function (table) - This point (___, ___) is the vertex of the parabola Graphing - Put the vertex you found in the center of your x - y chart. - Choose 2 x -values less than and 2 x -values more than your vertex. - Plug in these x values to get 4 more points. - Graph all 5 points OR Find the Y-INTERCEPT AND REFLECT OVER THE AXIS OF SYMMETRY Find the vertex of each parabola. Graph the function and find the requested information for numbers 5-8. 5) f(x) = 2x 2 – 3 a = ____, b = ____, c = ____ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 y HINT : THERE IS NO MIDDLE TERM Direction of opening? _______ Axis of symmetry: ________ Vertex: _______ Max or min? _______ Y intercept ________ Reflect y Intercept________ Compare to the graph of y = x 2 _________________________ 2
YOU CAN ALWAYS MAKE A TABLE OF VALUES TO GRAPH!!!!! 6.) f(x)= x 2 + 2 x + 3 a = ____, b = ____, c = ____ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 y Direction of opening? _______ Axis of symmetry: ________ Vertex: _______ Max or min? _______ Y intercept ________ Reflect y Intercept________ Compare to the graph of y = x 2 _________________________ 7.) h(x) = 2x 2 + 8x + 1 a = ____, b = ____, c = ____ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2