Find the vertex, x-intercept and y-intercept. F(x)=-.0.25x^2-3x
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the trick is to complete the square;
first change .25 to 1/4 - easier to work with
then isolate the 1/4 in the equation, such that 1/4(x^2 - 12x )
now complete the square.....12 divided by 2 and square becomes...
y = 1/4 (x^2 -12x +36 -36)
Now factor the FIRST three terms (ignore the 1/4 and -36 for the moment)....
y = 1/4 {(x - 6)^2 -36 }
take out the - 36 from the { brackets....
y = 1/4 (x - 6)^2 - 9 TO CHECK: re-expand to see if you have the original equation...TIP always do this.
VERTEX is (6, -9) ie the graph is a parabola opening UP so this vertex is a MINIMUM ( you can graph and see this)
X-INTERCEPT when y = 0, solve: 0 = 1/4(x - 6)^2 -9 becomes 9 = 1/4 (x - 6)^2
multiply by 4....36 = (x - 6)^2
sq root: plus or minus 6 = x - 6, X= 12 or X = 0 (x intercepts)
Y-INTERCEPT when x = 0, so y = 1/4(0 -6)^2 - 9 becomes y = 1/4(36) - 9 = 0, Y=0 (y intercept)
HIGHLY recommend graphing the original equation or the 'standard form' that gives you the Vertex, and see if everything matches, ie Vertex, x and y intercepts ( use trace calc to find the x-intercepts, also called the zeros, solution, roots.
first change .25 to 1/4 - easier to work with
then isolate the 1/4 in the equation, such that 1/4(x^2 - 12x )
now complete the square.....12 divided by 2 and square becomes...
y = 1/4 (x^2 -12x +36 -36)
Now factor the FIRST three terms (ignore the 1/4 and -36 for the moment)....
y = 1/4 {(x - 6)^2 -36 }
take out the - 36 from the { brackets....
y = 1/4 (x - 6)^2 - 9 TO CHECK: re-expand to see if you have the original equation...TIP always do this.
VERTEX is (6, -9) ie the graph is a parabola opening UP so this vertex is a MINIMUM ( you can graph and see this)
X-INTERCEPT when y = 0, solve: 0 = 1/4(x - 6)^2 -9 becomes 9 = 1/4 (x - 6)^2
multiply by 4....36 = (x - 6)^2
sq root: plus or minus 6 = x - 6, X= 12 or X = 0 (x intercepts)
Y-INTERCEPT when x = 0, so y = 1/4(0 -6)^2 - 9 becomes y = 1/4(36) - 9 = 0, Y=0 (y intercept)
HIGHLY recommend graphing the original equation or the 'standard form' that gives you the Vertex, and see if everything matches, ie Vertex, x and y intercepts ( use trace calc to find the x-intercepts, also called the zeros, solution, roots.
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You forgot to include your answers.