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Q: Always use the vertex and at least points to graph each quadratic equation?

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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.

The vertex form for a quadratic equation is y=a(x-h)^2+k.

The vertex.

D

y=2(x-3)+1

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.

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 vertex must be half way between the two x intercepts

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)

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.

it is a vertices's form of a function known as Quadratic

vertex

It if the max or minimum value.

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.

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.

Do you have a specific vertex fraction? vertex = -b/2a wuadratic = ax^ + bx + c

2 AND 9

(1/2, 71 and 3/4)or(0.5, 71.75)

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.

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.

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).

0,0

3

It is (1, 1).

Pick at least six points (negative x values and some positive x values). You can also find its vertex (x=-b divided by 2a).