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For a quadratic function, how to find the coordinates of the vertex of its graph?

By completing square, we can rewrite y = ax 2 + bx + c i n the form of y = a ( x - h ) 2 + k , so as to find h and k. = a ( x 2 + ) + c. (b) For y = ax 2 + bx + c , the vertex of the graph is. y -coordinate of Vertex Easy Memory Tips :. Move outside the brackets.

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For a quadratic function, how to find the coordinates of the vertex of its graph?

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  1. By completing square, we can rewritey= ax2+bx+cin the form of y= a(x-h)2+k, so as to find h and k. = a(x2+)+c (b) For y= ax2+bx+c, the vertex of the graph is y-coordinate of Vertex Easy Memory Tips: Move outside the brackets ( , ). = a(x+ )2-+c ∴h = , = a[x2+ + - ]+c = a[x- ]2+ k = Since ∆=b2-4ac, we can memorize as . 2. Functions and Graphs For a quadratic function, how to find the coordinates of the vertex of its graph? (a) For y= a(x-h)2+k, the vertex of the graph is (h , k). h k - y= ax2+bx+c Take out the coefficient of x2 in the first two terms Add up the square of half the coefficient of x

  2. E.g. h =, Completing Square k = 2. Functions and Graphs For a quadratic function, how to find the coordinates of the vertex of its graph? For y= a(x-h)2+k, the vertex of the graph is (h , k), where . For the functiony = x2-12x+40, find the coordinates of the vertex of its graph. 40 +4 y = x2-12x+ = x2-12x+36+4 36 = x2-2(6)x+62 +4 = (x-6)2 +4 k h ∴ The coordinates of the vertex of its graph are (6 , 4).

  3. E.g. Algebraic Method 2. Functions and Graphs For a quadratic function, how to find the coordinates of the vertex of its graph? For y= a(x-h)2+k, the vertex of the graph is (h , k), where . k = h =, For the functiony = x2-12x+40, find the coordinates of the vertex of its graph. = = x-coordinate = = = y-coordinate = ∴ The coordinates of the vertex of its graph are (6 , 4). The answer is the same as using completing square, but using the formula is more efficient.

  4. E.g. h =, Take outfrom the bracket Completing Square k = are ( , ). = 2[x- ]2- = 2(x+ )2- 2. Functions and Graphs For a quadratic function, how to find the coordinates of the vertex of its graph? For y= a(x-h)2+k, the vertex of the graph is (h , k), where . For y = 2x2+2x-1, find the coordinates of the vertex of its graph. y = 2x2+2x-1 22 Take out the coefficient of x2 in the first two terms = 2(x2+x)-1 Add up the square of half the coefficient of x ] [ 2 = 2[x2+x+ ] -1 + k h ∴ The coordinates of the vertex of its graph

  5. E.g. Algebraic Method ( , ). 2. Functions and Graphs For a quadratic function, how to find the coordinates of the vertex of its graph? For y= a(x-h)2+k, the vertex of the graph is (h , k), where . k = h =, For y = 2x2+2x-1, find the coordinates of the vertex of its graph. x-coordinate= = = y-coordinate= = = ∴The coordinates of the vertex of the graph are The answer is the same as using completing square, but using the formula is more efficient.

  6. E.g. Algebraic Method Substitute x= into the equation, we have ∴ The coordinates of the vertex of the graph are( , ). -1-1 2( )2+2( )-1 2. Functions and Graphs For a quadratic function, how to find the coordinates of the vertex of its graph? For y= a(x-h)2+k, the vertex of the graph is (h , k), where . k = h =, Fory = 2x2+2x-1, find the coordinates of the vertex of its graph. It is hard to memorize the formula for the y-coordinate. We can find the x-coordinate first and then substitute it into the equation to find the y-coordinate. x-coordinate = = = 2x2-2x+1 y =

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