Q:

Part l:find the x-intercepts of the parabola and write them as ordered pairs. Hint: the x-intercepts are the points at which the function crosses the x-axis and y=0. Show your workPart ll:Write the equation y=(x-4)(x+2) in standard form. Show your work.Part lll:with the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertex. Hint: the x-value of the vertex is -b/2a. Show your workPart lV:substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex. Then, write the coordinates of the vertex

Accepted Solution

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Answer:Part 1) The x-intercepts are the points (-2,0) and (4,0)Part 2) [tex]y=x^{2} -2x-8[/tex]Part 3) The x-coordinate of the vertex is 1Part 4) The y-coordinate of the vertex is -9 and the coordinate of the vertex is the point (1,-9)Step-by-step explanation:we have[tex]y=(x-4)(x+2)[/tex]Part 1) Find the x-intercepts of the parabola and write them as ordered pairsThe x-intercepts are the values of x when the value of y is equal to zerosoFor y=0[tex](x-4)(x+2)=0[/tex]For x=4 and x=-2 the equation is equal to zerothereforeThe x-intercepts are the points (-2,0) and (4,0)Part 2) Write the equation y=(x-4)(x+2) in standard formThe quadratic equation in standard form is equal to[tex]y=ax^{2} +bx+c[/tex]applying distributive property[tex]y=(x-4)(x+2)\\\\y=x^{2}+2x-4x-8\\\\ y=x^{2} -2x-8[/tex]where[tex]a=1, b=-2,c=-8[/tex]Part 3) With the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertexwe know thatthe x-value of the vertex is -b/2awe have[tex]a=1, b=-2,c=-8[/tex]substitute[tex]-\frac{b}{2a}=-\frac{(-2)}{2(1)}=1[/tex]thereforeThe x-coordinate of the vertex is 1Part 4) Substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex.we have[tex]y=(x-4)(x+2)[/tex]For x=1substitute and solve for y[tex]y=(1-4)(1+2)[/tex][tex]y=(-3)(3)[/tex][tex]y=-9[/tex]thereforeThe y-coordinate of the vertex is -9The coordinate of the vertex is the point (1,-9)