Question 362085
Convert to vertex form by completing the square.
{{{y=7x^2+21x-378}}}
{{{y=7(x^2+3x)-378}}}
{{{y=7(x^2+3x+9/4)-378-7(9/4)}}}
{{{y=7(x+3/2)^2-1512/4-63/4}}}
{{{y=7(x+3/2)^2-1575/4}}}
The vertex is ({{{-3/2}}},{{{-1575/4}}}).
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To find the y-intercept, set {{{x=0}}} and solve for {{{y}}}.
{{{y=7x^2+21x-378}}}
{{{y=7(0)+21(0)-378}}}
{{{y=-378}}}
({{{0}}},{{{-378}}})
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To find the x-intercept, set {{{y=0}}} and solve for {{{x}}}.
{{{y=7(x+3/2)^2-1575/4}}}
{{{7(x+3/2)^2-1575/4=0}}}
{{{7(x+3/2)^2=1575/4}}}
{{{(x+3/2)^2=225/4}}}
{{{x+3/2=0 +- 15/2}}}
{{{x=-3/2 +- 15/2}}}
{{{x[1]=12/2=6}}}
{{{x[2]=-18/2=-9}}}
({{{6}}},{{{0}}})
({{{-9}}},{{{0}}})
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{{{drawing(300,300,-10,10,-400,100,grid(1),circle(-9,0,.5),circle(6,0,.5),circle(0,-378,.5),circle(-3/2,-1575/4,.5),graph(300,300,-10,10,-400,100,7x^2+21x-378))}}}