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. Standard form uses the coefficients a, b, and c, vertex form identifies the vertex point (h, k), and intercept form finds the x-intercepts p and q to define the parabola.

1. 3 Forms of a Quadratic Function!

2. Key IdeasThe axis of symmetry divides the parabola into mirror images and passes through the vertex.

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.

7. a<0; the graph opens down.Standard Formf(x) = ax^2 + bx + c

8. Y=2x^2-8x+6Step 2: Find the vertex: x= -b/2a= -(-8)/2(2) X = 2 y= 2(2)^2-8(2)+6 y = -2Step 1: Identify coefficients: a=2 b=-8 c=6 a>0 so the parabola opens upStep 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=2Step 5: Draw parabola through the points.Step 6: Label the points(3,0)(1,0)(2,-2)

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

10. Y=2(x-3)^2-3Step 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=3Step 5: Label the points(4,-1)(2,-1)(3,-3)

11. Intercept Formf(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=1Step 1: Plot x-intercepts x=3 and x=-1Step 5: Label the points.Step 4: Connect the points.(1,-8)