This function is the quadratic function of the type xf(y)=ay^2+by+cxf(y)=ay2+by+c. This when written in the form x=a(y-k)^2+hx=a(y−k)2+h has (h,k)(h,k) as vertex and y-k=0y−k=0 i.e. y=ky=k as axis of symmetry.
To draw the graph, we select a few values of yy around kk i.e. both sides of kk - less than this as well as greater than this, to find corresponding values of xx and then draw graph.
Here we have x=5y^2-20y+23x=5y2−20y+23
= 5(y^2-4y)+235(y2−4y)+23 and completing square
= 5(y^2-4y+4)-5xx4+235(y2−4y+4)−5×4+23
= 5(y-2)^2+35(y−2)2+3
Hence vertex is (3,2)(3,2) and axis of symmetry is y-2=0y−2=0 or y=2y=2.
Selecting values y=-6,-4,-2,0,2,4,6,8,10y=−6,−4,−2,0,2,4,6,8,10 and putting them in x=5(y-2)^2+3x=5(y−2)2+3, we get x=323,183,83,23,3,23,83,183,323x=323,183,83,23,3,23,83,183,323and graph drawn to scale appears as
graph{5(y-2)^2+3-x=0 [-3.26, 76.74, -16.84, 23.16]}
However it will look better when xx-axis is compressed (i.e.not drawn to scale) as follows
graph{5(y-2)^2+3-x=0 [-10, 350, -10, 10]}
