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Graphing a quadratic with reflection and vertical stretch

Brian McLogan 116,612 lượt xem 9 years ago
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👉 Learn how to graph quadratic equations in vertex form. A quadratic equation is an equation of the form y = ax^2 + bx + c, where a, b and c are constants. The graph of a quadratic equation is in the shape of a parabola which can either face up or down (if x is squared in the equation) or face left or right (if y is squared).

To graph a quadratic equation, we need to know some essential parts of the graph including the vertex and the transformations. The vertex of a parabola is the turning point of the parabola. It is the point on the parabola at which the curve changes from increasing to decreasing or vice-versa. The transformation can be a vertical/horizontal shift, a stretch/compression or a refection.

Given a quadratic equation in the vertex form i.e. y = a(x - h)^2 + k, the vertex of the parabola formed by the equation is given by (h, k). Knowing the vertex of the graph and the parent graph, we can then apply the required transformation to obtain the required graph.

'h' in the vertex signifies the number of units left or right the the graph of the quadratic equation is shifted. 'k' in the vertex signifies the number of units up or down the the graph of the quadratic equation is shifted.

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Organized Videos:
✅How to graph a Quadratic in Vertex Form
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpht5dmr5EVXcF2-K0pOvwf
✅Identify the Vertex of a Quadratic
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoRLf4Sd1N6_Kjb5LTJ5DLv
✅Complete the Square then Graph | Hard
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMprnu6NjJjDqmzZ-7CZ19fi
✅Complete the Square then Graph | Easy
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqTGl0N6eLRFU3Lhmi2j-yg
✅Graph a Quadratic in Vertex Form with Vertical Shift Only
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpZfx78nH1BTuSDYUKHBmrH
✅Graph a Quadratic in Vertex Form with Stretch and Compression
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMouYj6AGltmfKoUqLw2agF7
✅Graph a Quadratic in Vertex Form with Horizontal Shift Only
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqy35AkcmJV5OkJaOLDOrYP
✅Graph a Quadratic in Vertex Form | Learn about
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqDfzQEDgwkj1zfWSNbL642
✅Graph a Quadratic in Vertex Form with Horizontal and Vertical Shifts
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrjzEHW-c_qRx2uE1Pk_NDx

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