User: What is the vertex of the parabola whose equation is y = (x + 1)2 + 3?

Weegy: Hint: Use ^ to indicate exponents in the future if you do not know how to write the exponents. Example: y = x^2 + 4x - 6 You have to complete the [ square to convert it into vertex form. y = x? + 4x - 6 Group. [ y = (x? + 4x) - 6 Factor y = (x? + 4x) - 6 Add placeholders. y = (x? + 4x + ___) - 6 - 1(___) Notice that the second blank is multiplied by -1 to account for what you had to add to complete the square. Take the coefficient of the x term: 4 Divide it by 2: 4 / 2 = 2 Square it: (2)? = 4 Add 4 to both blanks. y = (x? + 4x + 4) - 6 - 1(4) x? + 4x + 4 is the expanded form of a perfect square binomial. Remember that (a + b)? = a? + 2ab + b?. Apply this to what you have. y = (x? + 4x + 4) - 6 - 1(4) y = (x + 2)? - 6 - 1(4) Simplify the rest. y = (x + 2)? - 6 - 4 y = (x + 2)? - 10 Remember that the vertex form is: y = a(x - h)? + k CHECK: y = (x + 2)? - 10 y = [(x)? + 2(x)(2) + (2)?] - 10 y = (x? + 4x + 4) - 10 y = (x?) + 1(4x) + 1(4) - 10 y = x? + 4x + 4 - 10 y = x? + 4x - 6 TRUE ANSWER: y = (x + 2)? - 10 is the vertex form. Given: y = (x + 2)? - 10 Means: h = -2 Means: k = -10 Means: a = 1 ANSWER: The vertex is at (-2, -10). Since the equation is a function of x and a is positive, the parabola opens upwards. Parabolas that open upwards or downwards have an axis of symmetry that is the same as the h coordinate of the vertex. ANSWER: The axis of symmetry is at x = -2. Remember that y-intercepts have x = 0. Find the value of y when x = 0 by substitution x with 0 in the original equation. y = x? + 4x - 6 y = 0? + 4(0) - 6 y = 0 + 0 - 6 y = -6 ANSWER: The y-intercept is at (0, -6). ] amartin123|Points 60|

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