SOLUTION: I need some help to find the y-intercept, the x intercepts, the turning point and sketch this equation: {{{ y=-x^2-5x+6 }}}

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Question 62027This question is from textbook Heinemann Maths Zone 9
: I need some help to find the y-intercept, the x intercepts, the turning point and sketch this equation: +y=-x%5E2-5x%2B6+This question is from textbook Heinemann Maths Zone 9

Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
I need some help to find the y-intercept, the x intercepts, the turning point and sketch this equation: +y=-x%5E2-5x%2B6+
To find the y intercept, let x=0 and solve for y.
y=-%280%29%5E2-5%280%29%2B6
y=0-0%2B6
y=6
The y-intercept is (0,6)
:
To find the x-intercept, let y=0 and factor and solve for x.
0=-x%5E2-5x%2B6
0=-x%5E2%2Bx-6x%2B6
0=%28-x%5E2%2Bx%29%2B%28-6x%2B6%29
0=-x%28x-1%29-6%28x-1%29
0=%28x-1%29%28-x-6%29
x-1=0 and -x-6=0
x-1+1=0+1 and -x-6+6=0+6
x=1 and -x=6
x=1 and x=-6
The x-intercepts are (1,0) and (-6,0)
:
To find the turning point or vertex use the formula highlight%28x=-b%2F2a%29
a=-1, b=-5 (and c=6, but you don't need it for this)
x=-%28-5%29%2F%282%28-1%29%29
x=-5%2F2
Substitute that in for x and find the y coordinate.
y=-%28-5%2F2%29%5E2-5%28-5%2F2%29%2B6
y=-%2825%2F4%29%2B25%2F2%2B6 LCD=4
y=-25%2F4%2B50%2F4%2B24%2F4
y=%28-25%2B50%2B24%29%2F4
y=49%2F4
The turning point is (-5/2, 49/4)
graph%28300%2C200%2C-10%2C10%2C-10%2C15%2C-x%5E2-5x%2B6%29
Happy Calculating!!!