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For for each quadratic function below use method of completing the Square or averaging the x-intercept to write the equation in the Graphing form. then, State Line of symmetry and give the vertex of each parabola. try to use the method at least one. [tex]a.f(x) = {x}^{2} + 6 x + 15[/tex][tex]b.y = {x}^{2} - 4x +9[/tex][tex]c.f(x) = {x}^{2} - 8x[/tex][tex]d.y = {x}^{2} + 7x - 2[/tex]

Sagot :

We have the expressions:

[tex]f(x)=x^2+6x+15[/tex][tex]y=x^2-4x+9[/tex][tex]f(x)=x^2-8x[/tex][tex]y=x^2+7x-2[/tex]

Now, with this we operate as follows:

a)

[tex]f(x)=x^2+6x+15=x^2+6x+9+15-9[/tex][tex]\Rightarrow(x+3)^2+6[/tex]

Then, the axis is x = -3 and the vertex (-3, 6)

b)

[tex]y=x^2-4x+9=x^2-4x+4+9-4[/tex][tex]\Rightarrow(x-2)^2+5[/tex]

Then, the vertex is (2, 5) and the axis is x = 2.

c)

[tex]f(x)=x^2-8x+4-4\Rightarrow(x-2)^2-4[/tex]

Then, the vertex is (2, -4) andd the axis is x = 2.

d)

[tex]y=x^2+7x-2=x^2+7x+\frac{49}{4}-2-\frac{49}{4}[/tex][tex]\Rightarrow(x+\frac{7}{2})^2-\frac{57}{4}[/tex]

Then, the vertex is (-7/2, -57/4) and the axis is -7/2.

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