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41 votes
7x+10=-x?
=
Who do I find the vertex and point to put on graph

User Contactabbas
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1 Answer

20 votes
20 votes

Answer:

  • vertex: (-7/2, -9/4)
  • other points: (0, 10), (-5, 0), (-2, 0)

Explanation:

The equation 7x +10 = -x² describes two points on a number line: x = -5 and x = -2.

Perhaps you want points to help you plot ...

y = x² +7x +10

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y-intercept

The y-intercept is easy to find: set x=0. What's left is the constant, y = 10. So, the point (0, 10) is one point on the graph.

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vertex

The vertex form of the equation is ...

y = a(x -h)² +k . . . . . . . . where (h, k) is the vertex, and 'a' is the vertical scale factor

If you expand this equation, you get ...

y = a(x² -2hx +h²) +k = ax² -2ahx +ah² +k

Comparing the coefficients to the equation you have, you can see that ...

1 = a

7 = -2ah

10 = ah² +k

Solving for h and k, we find ...

7 = -2(1)h ⇒ h = -7/2

10 = (1)(-7/2)² +k ⇒ k = 10 -49/4 = -9/4

With these values, we can write the vertex form equation as ...

y = (x +7/2)² -9/4

The vertex is (x, y) = (-7/2, -9/4).

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factored form

The equation can be factored by looking for factors of 10 that have a sum of 7. Such values are 2 and 5.

y = x² +7x +10 = (x +2)(x +5)

The x-intercepts are the values of x that make these factors zero.

x +2 = 0 ⇒ x = -2

x +5 = 0 ⇒ x = -5

This tells you two other points on the graph are (-2, 0) and (-5, 0).

7x+10=-x? = Who do I find the vertex and point to put on graph-example-1
User SeventhWarhawk
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