The document discusses three forms of quadratic functions - standard form, vertex form, and intercept form - and provides examples of how to write quadratic functions in each form and the steps to graph each by finding the vertex, axis of symmetry, and intercepts. The standard form is ax^2 + bx + c, the vertex form is a(x-h)^2 + k, and the intercept form is a(x-p)(x-q), with each using different variables to indicate the features of the parabolic graph.

1. 3 Forms of a Quadratic Function!

3. a tells whether the graph opens up or down and whether the graph is wide or narrow.

4. H controls horizontal translations.

5. K controls vertical translations

6. a>0; the graph opens up.

8. Y=2x^2-8x+6 Step 2: Find the vertex: x= -b/2a= -(-8)/2(2) X = 2 y= 2(2)^2-8(2)+6 y = -2 Step 1: Identify coefficients: a=2 b=-8 c=6 a>0 so the parabola opens up Step 4: Plot 2 more points. Go to the left by one and up 2. Then do it again for the right side. Step 3: Draw axis of symmetry x=-b/2a x=2 Step 5: Draw parabola through the points. Step 6: Label the points (3,0) (1,0) (2,-2)

9. Vertex Form f(x) = a (x-h)^2 + k

10. Y=2(x-3)^2-3 Step 3: Plot 2 more points. Go to the left by one and up 2. Then do it again for the right side. Step 1: Determine vertex: (h,k)= (3, -3) Step 4: Connect the points to form a parabola. Step 2: Plot the vertex, (3,-3) Draw the axis of symmetry. x=h so x=3 Step 5: Label the points (4,-1) (2,-1) (3,-3)

11. Intercept Form f(x) = a (x-p) (x-q)

12. Y= 2(x-3)(x+1) (-1,0) (3,0) Step 2: Find the coordinates of the vertex and plot them. ((p+q)/2, f(p+q)/2) x= (3-1)/2= 2/2=1 x=1 Y= 2(1-3)(1+1) Y= 2(-2)(2) y=-8 Vertex= (1,-8) Step 3: Plot the axis of symmetry. Axis of symmetry is x=(p+q)/2 x=1 Step 1: Plot x-intercepts x=3 and x=-1 Step 5: Label the points. Step 4: Connect the points. (1,-8)