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# 3 Forms Of A Quadratic Function

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### 3 Forms Of A Quadratic Function

1. 1. 3 Forms of a Quadratic Function!<br />
2. 2. Key Ideas<br /><ul><li>The axis of symmetry divides the parabola into mirror images and passes through the vertex.
3. 3. a tells whether the graph opens up or down and whether the graph is wide or narrow.
4. 4. H controls horizontal translations.
5. 5. K controls vertical translations
6. 6. a>0; the graph opens up.
7. 7. a<0; the graph opens down.</li></li></ul><li>Standard Form<br />f(x) = ax^2 + bx + c<br />
8. 8. Y=2x^2-8x+6<br />Step 2:<br /> Find the vertex:<br /> x= -b/2a= -(-8)/2(2)<br /> X = 2<br /> y= 2(2)^2-8(2)+6<br /> y = -2<br />Step 1: <br /> Identify coefficients:<br /> a=2 b=-8 c=6<br /> a>0 so the parabola opens up<br />Step 4:<br /> Plot 2 more points. <br />Go to the left by one and up 2. Then do it again for the right side.<br />Step 3:<br /> Draw axis of symmetry<br /> x=-b/2a<br /> x=2<br />Step 5:<br /> Draw parabola through the points.<br />Step 6: <br /> Label the points<br />(3,0)<br />(1,0)<br />(2,-2)<br />
9. 9. Vertex Form<br />f(x) = a (x-h)^2 + k<br />
10. 10. Y=2(x-3)^2-3<br />Step 3:<br /> Plot 2 more points. <br />Go to the left by one and up 2. Then do it again for the right side.<br />Step 1:<br /> Determine vertex:<br /> (h,k)= (3, -3)<br />Step 4:<br /> Connect the points to form a parabola.<br />Step 2:<br /> Plot the vertex, (3,-3)<br /> Draw the axis of symmetry.<br /> x=h so x=3<br />Step 5:<br /> Label the points<br />(4,-1)<br />(2,-1)<br />(3,-3)<br />
11. 11. Intercept Form<br />f(x) = a (x-p) (x-q)<br />
12. 12. Y= 2(x-3)(x+1)<br />(-1,0)<br />(3,0)<br />Step 2:<br /> Find the coordinates of the vertex and plot them.<br /> ((p+q)/2, f(p+q)/2)<br /> x= (3-1)/2= 2/2=1<br /> x=1<br /> Y= 2(1-3)(1+1)<br /> Y= 2(-2)(2)<br /> y=-8<br /> Vertex= (1,-8)<br />Step 3: <br /> Plot the axis of symmetry. <br /> Axis of symmetry is x=(p+q)/2<br /> x=1<br />Step 1:<br /> Plot x-intercepts<br /> x=3 and x=-1<br />Step 5:<br /> Label the points.<br />Step 4:<br /> Connect the points.<br />(1,-8)<br />