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I would use the alternate parabolic equation (y-k)2 = a (x-h). You can plug in the coordinates of the vertex (h, k)--h is the x coordinate of the vertex and k is the y coordinate of the vertex.

Now you are left with an equation with an x and y, which are fine, but also an a, which we still have to get rid of. The a describes how steeply the parabola increases. To find the actual number, plug the other point you were given into the equation (where the x and y are). How you are left with one equation and one variable, so you can solve for a = some number.

Now return to the beginning of the previous step, when you had and x, y, and a in your equation. Keep the x and y in their original positions, but replace a with the number you just found.

Q: How do you find an equation of a parabola using the vertex and a point it passes through?

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3

the equation of a parabola is: y = a(x-h)^2 + k *h and k are the x and y intercepts of the vertex respectively * x and y are the coordinates of a known point the curve passes though * solve for a, then plug that a value back into the equation of the parabola with out the coordinates of the known point so the equation of the curve with the vertex at (0,3) passing through the point (9,0) would be.. 0 = a (9-0)^2 + 3 = 0 = a (81) + 3 = -3/81 = a so the equation for the curve would be y = -(3/81)x^2 + 3

A parabola with vertex (h, k) has equation: y = a(x - h)² + k With vertex (-3, -1) this becomes: y = a(x - -3)² + -1 = a(x + 3)² - 1 The point (4, 0) is on this parabola so: 0 = a(4 + 3)² - 1 → 7²a = 1 → a = 1/49 Thus the coefficient of x² is 1/49.

f(x)=x^2

Suppose the equation of the parabola is y = ax2 + bx + c where a, b, and c are constants, and a â‰ 0. The roots of the parabola are given by x = [-b Â± sqrt(D)]/2a where D is the discriminant. Rather than solve explicitly for the coordinates of the vertex, note that the vertical line through the vertex is an axis of symmetry for the parabola. The two roots are symmetrical about x = -b/2a so, whatever the value of D and whether or not the parabola has real roots, the x coordinate of the vertex is -b/2a. It is simplest to substitute this value for x in the equation of the parabola to find the y-coordinate of the vertex, which is c - b2/2a.

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please help

0,0

Y=3x^2 and this is in standard form. The vertex form of a prabola is y= a(x-h)2+k The vertex is at (0,0) so we have y=a(x)^2 it goes throug (2,12) so 12=a(2^2)=4a and a=3. Now the parabola is y=3x^2. Check this: It has vertex at (0,0) and the point (2,12) is on the parabola since 12=3x2^2

Use this form: y= a(x-h)Â² + k ; plug in the x and y coordinates of the vertex into (h,k) and then the other point coordinates into (x,y) and solve for a.

The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y

Vertex form is denoted by: y=a(x-h)2+k Where (h,k) is the vertex. So, we have: y=a(x-2)2+3 (This super\subscript thing is annoying). Plug in the values for x and y for the point in the equation and you have your answer.

3

Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.

the equation of a parabola is: y = a(x-h)^2 + k *h and k are the x and y intercepts of the vertex respectively * x and y are the coordinates of a known point the curve passes though * solve for a, then plug that a value back into the equation of the parabola with out the coordinates of the known point so the equation of the curve with the vertex at (0,3) passing through the point (9,0) would be.. 0 = a (9-0)^2 + 3 = 0 = a (81) + 3 = -3/81 = a so the equation for the curve would be y = -(3/81)x^2 + 3

We will be able to identify the answer if we have the equation. We can only check on the coordinates from the given vertex.

-2

The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.