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2. How do you find the vertex of a parabola in standard form?

   socratic.org/questions/how-do-you-find-the-vertex-of-a-parabola-in-standard-form

   Refer to the explanation. The standard form of a parabola is y=ax^2++bx+c, where a!=0. The vertex is the minimum or maximum point of a parabola. If a>0, the vertex is the minimum point and the parabola opens upward. If a<0, the vertex is the maximum point and the parabola opens downward. To find the vertex, you need to find the x- and y-coordinates. The formula for the axis of symmetry and the ...

3. Vertex Form of a Quadratic Equation - Algebra | Socratic

   socratic.org/algebra/quadratic-equations-and-functions/vertex-form-of-a...

   How do you find the standard form of the equation for the parabola with vertex (4,0) and passing through the point (1,2)? How do you find the vertex of #y = 4x^2 + 8x + 7#? How do you find the vertex of #y = -3x^2 + 12x – 7#?

4. How do you find the vertex, focus and directrix of - Socratic

   socratic.org/questions/how-do-you-find-the-vertex-focus-and-directrix-of-y-2-8x

   The vertex is at the point (0,0) The focus is at the point (-2, 0) The equation of the directrix line is x = 2 Let's begin by writing this in the form, x = ay² + by + c: x =(-1/8)y² Please recognize that this is a parabola that is rotated counterclockwise 90° so that it opens to the left. We know that it is rotated, because it uses "y" as the dependent variable. We know that it opens to the ...

5. How do you find the focus, vertex, and directrix of - Socratic

   socratic.org/questions/how-do-you-find-the-focus-vertex-and-directrix-of-y-2-4x

   Its vertex is (0, 0) Its focus is (-1, 0) Its directrix is x=1 given - y^2=-4x It is in the form y^2=-4ax If it is so, then - Its vertex is (0, 0) Its focus is (-a, 0) Its directrix is x=a Apply this in the given equation For better understanding the given equation can be written as y^2=4*(-1)*x Then- Its vertex is (0, 0) Its focus is (-1, 0) Its directrix is x=1

6. How do you find the vertex of a parabola without graphing?

   socratic.org/questions/how-do-you-find-the-vertex-of-a-parabola-without-graphing

   Assuming the parabola has not been rotated the vertex of the parabola occurs where the derivative of its function is equal to zero. Determine the general form of the derivative (this should be a linear function in terms of x) Set the general form of the derivative to zero and solve for x Substitute the value you obtained for x back into the expression for the parabola to get the y component of ...

7. How do you find the vertex of a parabola given by the equation

   socratic.org/questions/how-do-you-find-the-vertex-of-a-parabola-given-by-the...

   How do you find the vertex form of a quadratic equation? How do you graph quadratic equations written in vertex form? How do you write #y+1=-2x^2-x# in the vertex form?

8. How do you find the vertex of a parabola using the axis of ... -...

   socratic.org/questions/how-do-you-find-the-vertex-of-a-parabola-using-the-axis...

   When you're given the quadratic equation of the parabola, you can find it's vertex using the axis of symmetry. The axis of symmetry in a quadratic equation would always be #x=-b/(2a)#. Here is an example of a quadratic equation #y=x^2-x+3# We can find the axis of symmetry by using #x=-b/(2a)#.

9. How do you find the vertex of a parabola f(x)=x^2 +10x-11 ... -...

   socratic.org/questions/how-do-you-find-the-vertex-of-a-parabola-f-x-x-2-10x-11

   Vertex of the parabola is at :color(blue)((-5, -36) The Standard form for the quadratic equation is : y=f(x)=ax^2+bx+c = 0 Given: y=f(x) = x^2+10x-11 where a=1; b=10 and c= -11 Find the x-coordinate of the vertex using the formula -b/(2a) x=-10/(2*1) rArr x=-5 To find the y-coordinate value of the vertex, set x=-15 in y= x^2+10x-11 y=(-5)^2+10(-5)-11 Simplify the right-hand side. rArr 25-50-11 ...

10. How do you find the vertex, focus and directrix of - Socratic

    socratic.org/questions/how-do-you-find-the-vertex-focus-and-directrix-of-y-2-16x

    The vertex is (0,0) because there are no translations in the function. When a parabola has a vertex at the origin, the focus is (0,p). The focus is always within the parabola, so a right-facing parabola has a focus to the right of the vertex. Our focus, therefore, would be 4 units to the right of the vertex and is (0,4).

11. How do you find the vertex of a parabola y=-[x]^2+1? - Socratic

    socratic.org/questions/how-do-you-find-the-vertex-of-a-parabola-y-x-2-1

    The vertex is at color(red)((0,1). > y = -x^2+1 The standard form of the equation for a parabola is y = ax^2+bx+c, so a = -1, b = 0, c = 1 The x-coordinate is at x = -b/(2a) = -0/(2(-1)) = 0 To find the y-coordinate of the vertex, substitute x =0 into the equation to get y = -(0)^2 +1 = 0+1 = 1 The vertex is at (0,1). graph{-x^2+1 [-3, 3, -5, 2]}