Question

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. $a.f(x) = {x}^{2} + 6 x + 15$$b.y = {x}^{2} - 4x +9$$c.f(x) = {x}^{2} - 8x$$d.y = {x}^{2} + 7x - 2$

Answer 1

We have the expressions:

$f(x)=x^2+6x+15$$y=x^2-4x+9$$f(x)=x^2-8x$$y=x^2+7x-2$

Now, with this we operate as follows:

a)

$f(x)=x^2+6x+15=x^2+6x+9+15-9$$\Rightarrow(x+3)^2+6$

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

b)

$y=x^2-4x+9=x^2-4x+4+9-4$$\Rightarrow(x-2)^2+5$

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

c)

$f(x)=x^2-8x+4-4\Rightarrow(x-2)^2-4$

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

d)

$y=x^2+7x-2=x^2+7x+\frac{49}{4}-2-\frac{49}{4}$$\Rightarrow(x+\frac{7}{2})^2-\frac{57}{4}$

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