<p>I'm having problems with parabolas. What do I need to know to understand how to do them. Can anyone give me a quick rundown on parabolas, or a link to one?</p>
<p>For f(x) = ax^2+bx+c (the standard form), where a, b and c are real numbers and a is nonzero the parabola has these properties</p>
<p>1) If a>0, then the parabola is concave upwards, which means it has a minimum point. (it looks like a U)</p>
<p>If a<0, then the parabola is concave downwards, which means it has a maximum point. (it looks like an upside down U)</p>
<p>2) the y-intercept is c</p>
<p>3) the axis of symmetry is the vertical line x = -b/2a </p>
<p>For f(x) = a(x-h)^2 + k, which is the vertex form has these properties</p>
<p>1) a indicates a reflection across the x-axis (if a negative sign shows), vertical stretch or compression (if a>0 it would be vertically stretched; if a<0 it would be vertically compressed)
2) h indicates the horizontal translation
this part is a bit tricky, because if you see (x-h) you might think that the graph is shifted to the left but in fact it is shifted to the right, because it truly is (x-(+h)).
the bottom line is (x-h) is translated to the right, and (x+h) is translated to the left.
3) k indicated the vertical translation, but nothing is tricky here. it is pretty intuitive. +k is upwards, -k is downwards.
4) a coefficient of x would indicate a horizontal stretch, if the coefficient is greater than 1 indicates a horizontal compression (notice how greater than 1 in this case is compression), if less than 1 but greater than 0 it indicates horizontal stretch (also notice how less than 1 it is stretch not compress in this case), and a negative number as a coefficient of x would indicate a horizontal reflection)
5) (h,k) is the vertex to the parabola.
6) last but not least, the modulus function is the function denoted by the absolute value sign |x^2| this indicates that the graph is above the x-axis.</p>
<p>does the SAT only test these 2 forms of the parabola? Also, for step 4 in the vertex form,for the coefficient of x where exactly in the equation are you talking about?
Is there anything else I need to know for parabolas?</p>
<p>Example: In the figure above, PQRS is a square and points Q,R,and O lie on the graph of y = ax^2,where a is a constant. If the area of the square is 64, what is the value of a?</p>
<p>How exactly would I figure this out?</p>
<p>I really appreciate this information on Parabolas . It was very helpful</p>
<p>pretty much yes.
consider this example</p>
<p>-4(-7x-3)^2 +10
- negative sign outside the brackets indicates a vertical reflection across the y-axis
- there is a vertical stretch by factor 4, which indicates that the graph is taller and thinner. ( just like stretching a rubber band)
- negative sign inside the bracket (or if there were no brackets at all) indicates a horizontal reflection across the x-axis)
- 7 indicates a horizontal compression
- 3 indicates a 3 units right translation/shift.
- shifted 10 units upwards.</p>
<p>the problem you just gave me is a very systematic problem that you’ll get used to it by practice.
You’ll have to play around with the equation here… </p>
<p>take the square root of 64 to figure out one side, so now the vertical distance is 8… the base of the square is also 8 but half of it is 4 so now we have the point (4,8)
y= ax^2
8=a4^2
8= 16a
a = 8/16 = 1/2</p>