Answer:
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
Step-by-step explanation:
Vertex is the minimum or maximum point of parabola
Vertex of parabola is (h,k)
Therefore, from given graph (-3,-2) is the lowest point.
Vertex of parabola is at (-3,-2).
Standard equation of parabola
[tex]y-k=a(x-h)^2[/tex]
Substitute the values
[tex]y-(-2)=a(x-(-3))^2=a(x+3)^2[/tex]
[tex]y+2=a(x+3)^2[/tex]
(-1,0) lies on the parabola.
Therefore, it satisfied the equation of parabola.
[tex]0+2=a(-1+3)^2=4a[/tex]
[tex]a=2/4=1/2[/tex]
Now, using the value of a
[tex]y+2=1/2(x+3)^2=1/2(x^2+6x+9)[/tex]
[tex]y+2=\frac{1}{2}x^2+3x+\frac{9}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9}{2}-2[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9-4}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{5}{2}[/tex]
By comparing with
[tex]y=ax^2+bx+c[/tex]
We get
[tex]a=\frac{1}{2}, b=3, c=5/2[/tex]
[tex]a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}[/tex]
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
