ALGEBRA II HONORS/GIFTED @ ALGEBRA II HONORS/GIFTED - SECTIONS 4-1 and 4-2 (Quadratic Functions and Transformations AND Standard and Vertex Forms) ALGEBRA II HONORS/GIFTED @ SECTION 4-1 : QUADRATIC FUNCTIONS and TRANSFORMATIONS SECTION 4-2 : STANDARD and VERTEX FORMS

1) Given f(x) = 2x2 a) Graph. b) What is the name of the graph? c) Locate the vertex. Is this a maximum or a minimum? 2) Graph f(x) = - 2x2

3) Given f(x) = x2 + 6x - 1 a) Graph. b) What is the name of the graph? c) Locate the vertex. Is this a maximum or a minimum? d) Find the y-intercept. e) Find the x-intercepts. Use the quadratic formula. f) What is the equation for the axis of symmetry? g) What is the range?

Describe how each function was translated from f(x) = x2. Graph. 4) f(x) = 0.5x2 5) f(x) = 2x2 6) f(x) = -x2 7) f(x) = -3x2

STANDARD FORM for a parabola : y = ax2 + bx + c If the sign of “a” is positive, the parabola turns up If the sign of “a” is negative, the parabola turns down The larger “a” is (regardless of sign), the more stretched the parabola is. The smaller “a” is, the more compressed it is.

In order to find the x-intercepts for a parabola, we can use the Quadratic Formula and solve for x. 8) Where does the x-coordinate for the vertex lie in relation to the x-intercepts? Therefore, we need to find the average of the two x-intercepts to find the x-coordinate of the vertex.

Therefore, you can find the x-coordinate for the vertex using the formula :

9) Find the coordinates of the vertex, equation for the axis of symmetry, the x-intercepts, and the y-intercept. Then, sketch the graph. What is the range? f(x) = x2 + 4x + 3

10) Find the coordinates of the vertex, equation for the axis of symmetry, the x-intercepts, and the y-intercept. Then, sketch the graph. What is the range? f(x) = -3x2 + 6x - 5

11) Graph y - 3 = 2(x – 1)2 on your graphing calculator. ALGEBRA II HONORS/GIFTED - SECTIONS 4-1 and 4-2 (Quadratic Functions and Transformations AND Standard and Vertex Forms) 11) Graph y - 3 = 2(x – 1)2 on your graphing calculator. a) Where is the vertex located? (1, 3) y - k = a(x – h)2 is called Vertex Form. The vertex is located at (h, k).

Write each function in Vertex Form. 12) y = x2 + 8x + 21 13) y = 8x2 + 40x - 37 14) y = -3x2 + 24x - 41