Determine, in Factored and Standard form, the equation for the quadratic function that has x-intercepts at 1 and -3 and a y-intercept at (0, −6). Show all your work.

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Determine, in Factored and Standard form, the equation for the quadratic function that has x-intercepts at 1 and -3 and a y-intercept at (0, −6). Show all your work.

James Etheridge · Accepted Answer

Step 1  The factored form of a quadratic function is y=a(x−x1)(x−x2), where (x1, 0) and (x2, 0) are the x-axis intercepts and a is a constant. Since we have been given that the x-intercept at 1 and -3, therefore, x1=1 and x2=−3. Put these values in y=a(x−x1)(x−x2)  y=a(x−1)(x−(−3))  =a(x−1)(x+3)  Since the y-intercept at (0, −6), so put (0, −6) in y=a(x−1)(x+3) to find the value of a.  −6=a(0−1)(0+3)  −6=−3a  2=a  Step 2  So, we obtained a=2. Thus, the factored form of a quadratic function is y=2(x−1)(x+3) Now, using the factored quadratic find the standard form of quadratic function. The standard form of a quadratic function is y=ax2+bx+c  y=2[x(x+3)−1(x+3)]  =2(x2+3x−x−3)  =2(x2+2x−3)  =2x2+4x−6  Factored form: y=2(x−1)(x+3); Standard form: yx2+4x−6

Determine, in Factored and Standard form, the equation for the

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