Graphing Parabolas: Determine Direction, Vertex, and Intercepts | Homework Help

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In summary, for problems 1 and 2, determine if the quadratic opens up or down, find the vertex using h=-b/2a, and find any intercepts by setting x=0 and solving for y. For problem 1, the parabola opens down and the vertex is (2,21). The x-intercepts are 1 and 3. For problem 2, the parabola opens up and the vertex is (-3/4, 23/8). The x-intercepts are -1/2 and 2.
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Homework Statement



For problems 1 and 2 determine if the quadratic opens up or down. Find the vertex. Find any intercepts and use these things to graph the quadratic equation.



Homework Equations



1. y=-3x^2+12x-9

2. y=2x^2+3x+2

The Attempt at a Solution


For number 1:
ok well i determined the parabola opens down becuase a(-3) is negitive. Hope i got that right.
Then i found the vertex by h=-b/2a becuase that will give me the x cordinate of the vertex so i did -12/2(-3) = 2. 2 is the x cordinate of the vertex so i put 2 into the original equation to get the y cordinate
Y=-3(2)^2+12(2)+9=21 i get 21 as my Y Cordinate.

Now for the intercepts i had a friend help me with this and he said there are no y int for a parabola...he also to me to take the equation -3x^2+12x-9=0 set it to 0 like that.

Then he told me to divid by 3 and get x^2-4x+3=0 then factor to get x=3 and x= 1 and those are my x ints for the parabola is this correct? any help would be greaty apriciated
 
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Everstar said:
Y=-3(2)^2+12(2)+9=21 i get 21 as my Y Cordinate.

Looks good so far except that at this stage you wrote +9, but in the original equation you wrote -9.

Everstar said:
Now for the intercepts i had a friend help me with this and he said there are no y int for a parabola...

That isn't true. The y intercept is the value of y=-3x2+12x-9 when x = 0. To find it, just set x equal to 0, and solve for y.

Everstar said:
he also to me to take the equation -3x^2+12x-9=0 set it to 0 like that. Then he told me to divid by 3 and get x^2-4x+3=0 then factor to get x=3 and x= 1 and those are my x ints for the parabola is this correct? any help would be greaty apriciated

That's right. (Another method is to use the quadratic formula.)
 

1. What is a parabola?

A parabola is a symmetrical curve formed by the graph of a quadratic equation, where the highest degree term is squared.

2. How do you graph a parabola?

To graph a parabola, you need to plot points on a coordinate plane. The points can be obtained by substituting different values for the variable in the quadratic equation and solving for the corresponding y-value. Once you have enough points, you can connect them to form a smooth curve.

3. What are the key features of a parabola?

The key features of a parabola are the vertex, which is the highest or lowest point on the curve, and the axis of symmetry, which is a vertical line that divides the parabola into two symmetrical halves. The vertex also represents the minimum or maximum point of the parabola, depending on the direction it opens.

4. How do you determine the direction of a parabola?

The direction of a parabola is determined by the coefficient of the squared term. If the coefficient is positive, the parabola opens upwards and has a minimum point. If the coefficient is negative, the parabola opens downwards and has a maximum point.

5. What is the significance of graphing parabolas?

Graphing parabolas is important in many fields of science and mathematics. It allows us to visualize and analyze quadratic equations, which are used to model various real-world phenomena such as projectile motion, population growth, and financial data. It also helps us understand the properties and behavior of parabolas, which have many practical applications in engineering and physics.

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