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stealth61 [152]
2 years ago
12

Convert the following quadratics from standard form to vetex form, then graph them.

Mathematics
1 answer:
9966 [12]2 years ago
4 0

1. Answer:  y = (x + 3)² - 4

<u>Step-by-step explanation:</u>

Vertex format is: y = a(x - h)² + k

y = x² + 6x + 5

y - 5 = x² + 6x       <em>subtracted 5 from both sides</em>

y - 5 + \bigg(\dfrac{6}{2}\bigg)^2 = x² + 6x + \bigg(\dfrac{6}{2}\bigg)^2    <em>completed the square</em>

y + 4 = (x + 3)²        <em>simplified</em>

y = (x + 3)² - 4        <em>subtracted 4 from both sides</em>

Equation is now in vertex form!

To graph the equation, plot the following points:

  • vertex (h, k) = (-3, -4)
  • y-intercept from the original equation (0, c) = (0, 5)
  • mirror image of y-intercept (-6, 5)

2. Answer:  y = -(x + 3)² + 2

<u>Step-by-step explanation:</u>

Vertex format is: y = a(x - h)² + k

y = -x² - 6x - 7

y + 7 = -x² - 6x       <em>added 7 to both sides</em>

-y - 7 = x² + 6x         <em>divided both sides by -1</em>

-y - 7 + \bigg(\dfrac{6}{2}\bigg)^2 = x² - 6x + \bigg(\dfrac{6}{2}\bigg)^2    <em>completed the square</em>

-y + 2 = (x + 3)²        <em>simplified</em>

y - 2 = -(x + 3)²        <em>divided both sides by -1</em>

y = -(x + 3)² + 2        <em>subtracted 4 from both sides</em>

Equation is now in vertex form!

To graph the equation, plot the following points:

  • vertex (h, k) = (-3, 2)
  • y-intercept from the original equation (0, c) = (0, -7)
  • mirror image of y-intercept (-6, -7)

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