Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.y, equals, x, squared, minus, 12, x, plus, 29y=x 2 −12x+29
Question
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.y, equals, x, squared, minus, 12, x, plus, 29y=x 2 −12x+29
Solution
The vertex of a parabola given by the equation y = ax^2 + bx + c is given by the point (h, k), where h = -b/2a and k is the value of y at x = h.
Given the equation y = x^2 - 12x + 29, we can see that a = 1 and b = -12.
So, h = -b/2a = -(-12)/(2*1) = 6.
To find k, we substitute h = 6 into the equation:
k = (6)^2 - 12*(6) + 29 = 36 - 72 + 29 = -7.
So, the vertex of the parabola is (6, -7).
Similar Questions
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.y, equals, minus, 3, x, squared, plus, 6, x, plus, 12y=−3x 2 +6x+12
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.y, equals, 2, x, squared, minus, 28, x, plus, 80y=2x 2 −28x+80
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.y, equals, x, squared, plus, 3y=x 2 +3
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.y, equals, minus, 3, x, squared, plus, 18, x, minus, 15y=−3x 2 +18x−15
The graph of the quadratic is a parabola that passes through the points , , and . What is the -coordinate of the vertex of the parabola?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.