MATH SOLVE

7 months ago

Q:
# Determine the equation of the graph, and select the correct answer below.parabolic function going down from the left through the point approximately negative three fourths comma zero and through the point zero comma negative two and turning at the point one comma negative three and going up through the point approximately two and three fourths comma zero and continuing towards infinityCourtesy of Texas Instruments y = (x + 1)2 + 3 y = (x + 1)2 − 3 y = (x − 1)2 − 3 y = (x − 1)2 + 3

Accepted Solution

A:

Answer:The equation of the parabolic function is :[tex]y=(x-1)^2-3[/tex]Step-by-step explanation:The standard equation of a parabola is given by:[tex]y=a(x-h)^2+k[/tex]where [tex](h,k)[/tex] represents the vertex of the parabola.From the graph shown in figure we can find the vertex of the parabola which is the minimum point of parabola and lies st point [tex](1,-3)[/tex]So, we can say: [tex](h,k)\rightarrow (1,-3)[/tex]Plugging in the values of vertex in standard equation of parabola,[tex]y=a(x-1)^2+(-3)[/tex]Simplifying the equation:[tex]y=a(x-1)^2-3[/tex]We can find value of [tex]a[/tex] by plugging in a point from the graph.Using point (0,-2) which lies on graph.Plugging in the given point.[tex]-2=a(0-1)^2-3[/tex][tex]-2=a-3[/tex]Adding 3 to both sides.[tex]-2+3=a-3+3[/tex][tex]1=a[/tex]∴ [tex]a=1[/tex]Plugging in [tex]a=1[/tex], the equation of parabola can be written as:[tex]y=(x-1)^2-3[/tex]