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Answered 2014-08-22 01:44:55
You should always use the vertex and at least two points to graph each quadratic equation. A good choice for two points are the intercepts of the quadratic equation.
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What different information do you get from vertex form and quadratic equation in standard form?
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
What is the equation for vertex form?
The vertex form for a quadratic equation is y=a(x-h)^2+k.
How do you find the x value of the vertex of a quadratic equation?
It depends on the level of your mathematical knowledge. One way is to differentiate the quadratic equation and find the value of x for which the derivative is 0. The advantage of this method is that it works for turning points of polynomials of all degrees. The disadvantage is that you need to know differentiation. For a quadratic, an alternative, and simpler way is to write the equation in the form: y = ax2 + bx + c Then the x value of the vertex is -b/2a
The number of solution a quadratic equation has?
A quadratic equation always has 2 solutions.In the instance of perfect squares, however, there will be just one number, which is a double root. Graphically, this is equivalent of the vertex of a parabola just barely touching the x-axis.
How would you use intercepts to find the vertex in a quadratic equation with two x intercepts?
The vertex must be half way between the two x intercepts
How do you find the vertex from a quadratic equation in standard form?
look for the interceptions add these and divide it by 2 (that's the x vertex) for the yvertex you just have to fill in the x(vertex) however you can also use the formula -(b/2a)
How does finding the vertex of a parabola help you when graphing a quadratic equation?
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.
What is the vertex form of a quadratic equation?
The formula for the vertex form is: f(x) = a(x-h)^2 + k Where (h,k) is the vertex. The equation also tells us the direction of opening, which is the a value, in this case opens up because a is positive. It tells us the step pattern, which when a is equal to one is always 1,3,5. However, when the a value is a number other than one, you muct multiply the value by 1,3,5.
What is the definition of a Vertex form of a quadratic function?
it is a vertices's form of a function known as Quadratic
What is the average of the two roots of quadratic equation?
In a quadratic y = ax² + bx + c, the roots are where y = 0, and the parabola crosses the x-axis. The average of these two roots is the x coordinate of the vertex of the parabola.
How do you graph a quadratic equation?
A quadratic equation is an equation with the form: y=Ax2+Bx+C The most important point when graphing a parabola (the shape formed by a quadratic) is the vertex. The vertex is the maximum or minimum of the parabola. The x value of the vertex is equal to -B/(2A). Once you have the x value, just plug it back into the original equation to get the corresponding y value. The resulting ordered pair is the location of the vertex. A parabola will be concave up (pointed downward) if A is +. It will be concave down (pointed upward) if A is -. It is often helpful to find the zeroes of a function when graphing. This can be done by factoring or using the quadratic formula. For every n units away from the vertex on the x-axis, the corresponding y value goes up (or down) by n2*A. Parabolas are symetrical along the vertex, which means that if one point is n units from the vertex, the point -n units from the vertex has the same y value. As an example take the following quadratic: 2x2-8x+3 A=2, B=-8, and C=3 The x value of the vertex is -B/2A=-(-8)/(2*2)=2 By plugging 2 into the original equation we get that the vertex is at (2,-5) 3 units to the right (x=5) has a y value of -5+32*2=13. This means that 3 units to the left (x=-1) has the same y value (-1,13). If you need a clearer explanation, ask a math teacher.
What is the vertex of the quadratic function?
It if the max or minimum value.
What is the vertex of x2-10x plus 21?
First, check to see if the equation can be simplified into bracket form. In this case, it can be simplified to (-x + 3)(-x + 7). These brackets identify the zeroes of the quadratic equation; the vertex is always in the middle of the zeros. To find the zeros, set the brackets equal to zero, and now x = 3, 7. 3+7/2 = 10/2 = 5, so the vertex occurs at x = 5. y at x = 5 is -4, so the vertex is (5, -4).
How do you convert vertex form to quadratic form?
Do you have a specific vertex fraction? vertex = -b/2a wuadratic = ax^ + bx + c
How do you do a parabola?
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
What is the vertex of the quadratic equation y equals x squared minus x plus 72?
(1/2, 71 and 3/4)or(0.5, 71.75)
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
Can you write a poem based on the standard form the axis of symmetry and the vertex of a quadratic equation?
Lewis Carroll wrote these lines about a quadratic:Yet what are all such gaieties to meWhose thoughts are full of indices and surds?x*x + 7x + 53 = 11/3
Vertex of a parabola?
The vertex of a parabola is found by using the solution of the equation -b/2a and putting it into the quadratic equation. a is the coefficient of x^2. b is the coefficient of the other x in the equation. Ex. y=2x^2+2x+1 -b/2a = -2/2(2) = -1/2 Now put -1/2 in the place of every x in the equation. y=2(-1/2)^2+2(-1/2)+1 The vertex is (-1/2, 1/2)
How do you graph a quadratic?
Pick at least six points (negative x values and some positive x values). You can also find its vertex (x=-b divided by 2a).
What is Y equals 2xsquared-12x plus 6?
"y = 2x2 - 12x + 6" is a quadratic equation which describes a parabola whose vertex occurs at the point (3, -12) and which has a range of -12 → ∞. It intercepts the x-axis at the points (3 - √6, 0) and (3 + √6, 0).
What is the y-coordinate of the vertex of the parabola that is given by the equation below?
We will be able to identify the answer if we have the equation. We can only check on the coordinates from the given vertex.
If two points have the same points then?
if two points have the same points then they make a vertex.
What things are significant about the vertex of a quadratic function?
It is a turning point. It lies on the axis of symmetry.
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