2
For example, the parabola y 2 = x 3 opens to the right, like a "C" Advertisement 3 Find the axis of symmetry Remember that the axis of symmetry is the straight line that passes through the turning point (vertex) of the parabola In the case of a vertical parabola (opening up or down), the axis is the same as the x coordinate of the vertexThe focus of a parabola can be found by adding to the ycoordinate if the parabola opens up or down Substitute the known values of , , and into the formula and simplify Find the axis of symmetry by finding the line that passes through the vertex and the focus
Graph the parabola y 3x 2
Graph the parabola y 3x 2-The axis of symmetry is located at y = k Vertex form of a parabola The vertex form of a parabola is another form of the quadratic function f(x) = ax 2 bx c The vertex form of a parabola is f(x) = a(x h) 2 k The a in the vertex form of a parabola corresponds to the a in standard form If a is positive, the parabola will open upwardsA cardioid (from the Greek καρδιά "heart") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius It can also be defined as an epicycloid having a single cuspIt is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center of inversion A cardioid can also be defined as the set of
2
Two numbers r and s sum up to 3 exactly when the average of the two numbers is \frac{1}{2}*3 = \frac{3}{2} You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2BxC The values of r and s are equidistant from the center by an unknown quantity uQ Find an equation for the line tangent to the curve y =x 5 at the point (2,9)Sketch the curve and A Differentiating the equation of parabola and substituting the point gives the slope at that pointWhat are the prices that will create a profit of $00 per day What is the lowest price needed to
Let us find the slope of parabola Step 2 Differentiate wrt 'x' dy/ dx = d/dx (ax²) dy/ dx = 2ax At x = 2 dy/ dx = 4a > (2) Step 3 Equate equation (1) and (2), we get 3 = 4a a = 3/ 4 Step 4 Substitute the values of a and x in the equation of parabola to get y y = ( 3/ 4) (2)² y = 3 Step 5 Substitute the values ofLet us understand with the help of examples Graphing Parabola Solved Examples Example 1 Draw a graph for the equation y = 2x 2 x 1 Solution The given equation is y = 2x 2 x 1 Here, a = 2, b = 1 and c = 1 Now substitute #a=3 # and #b=2# in the equation #y=ax^2bxc# #y=3x^22xc# We have to find the value of #c# We know the parabola is passing through the point #2,15# We shall use this information to find the value of #c# #3(2)^22(2)c=15# #124c=15# #8c=15# #c=158=7# #c=7# Now substitute #a=3 #, #b=2# and #c=7# in the equation #y=ax^2
Graph the parabola y 3x 2のギャラリー
各画像をクリックすると、ダウンロードまたは拡大表示できます
 |  |  |
 |  | |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  | |
 |  |  |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  | |
 |  |  |
 | ||
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  | |
 |  | |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  |  |
 |  |  |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 | ||
 |  |  |
 |  |  |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 | ||
 |  |  |
 |  |  |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  | |
 |  | |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  |  |
 |  |  |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  | |
 |  |  |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  |  |
 |  |  |
 |  | |
「Graph the parabola y 3x 2」の画像ギャラリー、詳細は各画像をクリックしてください。
 |  | |
 |  |
Examples with Detailed Solutions Example 1 Graph of parabola given x and y intercepts Find the equation of the parabola whose graph is shown below Solution to Example 1 The graph has two x intercepts at \( x = 1 \) and \( x = 2 \) Hence the equation of the parabola may be written as \( y = a(x 1)(x 2) \) We now need to find the coefficient \( a \) using the y intercept at \( (0,2Y = –2(x 5)2 – 3 39 y = –5(x 2)2 5 49A model of the daily profits p of a gas station based on the price per gallon g is p = 15,000g2 34,500g – 16,800 Find the price that will the maximum profits What is the maximum profit?
Incoming Term: is y x 2 a parabola, y 2 4x parabola, x 2 4y parabola, graph the parabola y 3x 2, y 2 4ax parabola, graph the parabola y x 2, x 2 4ay parabola, parametric equation of parabola y x 2, graph the parabola y 2x 2, for the parabola y 2 4ax, y ax 2 parabola, if the parabola y 2 4ax,
