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Math smarties needed!

Math smarties needed!-example-1
Math smarties needed!-example-1
Math smarties needed!-example-2

1 Answer

2 votes

Answer:

1.
y = (x + 2)(x + 3)

2.
y = -x(x + 4)

Explanation:

We can find the factored form of the graphed quadratic functions by:

1) Expressing each one in vertex form

2) Expanding and refactoring to rewrite in factored form

1. We know that vertex form is:


y = a(x-h)^2 + k,

where
a determines the parabola's direction and width (
a=1 being the same as a standard parabola), and
(h,k) is the parabola's vertex.

The vertex of this parabola is (-3, -4).

↓ plugging these values into the vertex form equation


y = 1(x - (-3))^2 + (-4)

↓ simplifying


y = (x + 3)^2 - 4

Now, we can expand and refactor this equation into factored form.

↓ expanding the squared term


y = (x^2 + 6x + 9) - 4

↓ simplifying


y = x^2 + 6x + 5

↓ factoring


\boxed{y = (x + 2)(x + 3)}

2. We can see that the vertex is at (-2, 4).

↓ plugging into the vertex form equation


y = -1(x - (-2))^2 + 4

Note that the parabola opens downward, so
a = -1.

↓ simplifying


y = -1(x +2)^2 + 4

↓ expanding the squared term


y = -1(x^2 +4x + 4) + 4

↓ incorporating the outer +4 into the distribution of -1


y = -1(x^2 + 4x + 4 - 4)

↓ simplifying


y = -1(x^2 + 4x)

↓ factoring


y = -1(x)(x + 4)

↓ simplifying


\boxed{y = -x(x + 4)}

User Mdmundo
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