Question

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

1. y=x^2+6x+5
2. y= -x^2-6x-7

Answer 1

1. Answer: y = (x + 3)² - 4

Explanation:

Vertex format is: y = a(x - h)² + k

y = x² + 6x + 5

y - 5 = x² + 6x subtracted 5 from both sides

y - 5 +
`\bigg((6)/(2)\bigg)^2` = x² + 6x +
`\bigg((6)/(2)\bigg)^2` completed the square

y + 4 = (x + 3)² simplified

y = (x + 3)² - 4 subtracted 4 from both sides

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

Explanation:

Vertex format is: y = a(x - h)² + k

y = -x² - 6x - 7

y + 7 = -x² - 6x added 7 to both sides

-y - 7 = x² + 6x divided both sides by -1

-y - 7 +
`\bigg((6)/(2)\bigg)^2` = x² - 6x +
`\bigg((6)/(2)\bigg)^2` completed the square

-y + 2 = (x + 3)² simplified

y - 2 = -(x + 3)² divided both sides by -1

y = -(x + 3)² + 2 subtracted 4 from both sides

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)