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Find the vertex of the following quardra...

Find the vertex of the following quardratic equations and plot the graph:
a. `y=x^2-8x`
b. `y=-2x^2+3`
c. `y=x^2-6x+4`

Text Solution

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a. `y=x^2-8x`, `a=1`, `b=-8`, `c=0`
Vertex, `x=-(b)/(2a)=-((-8)/(2xx1))=4`
At `x=4`, `y=4^2-8xx4=-16`,
At `x=0`, `y=0`
At `x=8`, `y=0`

b. `y=-2x^2+3`, `a=-2`, `b=0`, `c=3`
Vertex, `x=-(b)/(2a)=0`, at `x=0`, `y=3`
At `x=1`, `y=1` and at `x=-1`, `y=1`

c. `y=x^2-6x+4`, `a=1`, `b=-6`, `c=4`
Vertex: `x=-(b)/(2a)=-((-6)/(2xx1))=3`
At `x=3`, `y=-5`,
at `x=0`, `y=4`, at `x=6`, `y=4`
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Knowledge Check

  • What is the slope of following straight lines corresponding to equations (a) y= 2x (b) y = - 6x (c) y=4x +2 (d) y = 6x -4

    A
    `2` , `-6` , `4` , `6`
    B
    `2` , `-6` , `4` , `2`
    C
    `3` , `-6` , `4` , `6`
    D
    `2` , `-6` , `2` , `6`