Question

13. The following quadratic function is written in general form: f(x)=x2-6x-7 a) Write the factored form b) Write the vertex form (also known as standard form). c) Find the y-intercept. Which of the three forms listed above is the most useful in identifying the y-intercept and why? d) Find the x-intercepts. Which of the three forms listed above is the most useful in identifying the x-intercepts and why? e) Find the vertex. Which of the three forms listed above is the most useful in identifying the vertex and why? f) Graph I -10 10 -107 Focus

Answer 1

-7x2=-7xxx fet lx=-6x 1 The giran quadratic function f(x)=x²-67-7 a) factcred form x2=6*- x²_7x+x=7 x(x-7)+1(x-7) (x-7)(8+) the factored form (x-7)(x+1) oby verrex form x²-68-7= by x²_6x=7y+7 x² - 6x +3² = 7+3²+y x² - 6x +9. & 16 ty x²=60+9 y +16 (x-3) ²=9+16 (66=3)²-16=y the verrex form y= (2x+6) ²16 (c) they Intercept =-7 The general form is useful in finding the g Intercept to comparing ax?tb etc with x²-60-7 ..=-7 which is the y Intercept of the quachatic function IC 1 )

Ти which are the Zeroes of the function d) the x Intercepts of the function are 1=7 and x=-1 The factored form is most useful finding the x Intercept " comparing Cx-2) (at-ß) with (x-7)(xH) 2=7 an ß=-1 x-1= 0x=7 I ti-o x=-1 The Zeroes of the functions are the x Intercepte e) The Verley form of a quadratic equation in y= = a (x=h3tk when Chik) is the vertex comparing * = (x-B)2-16 h,=3 and K=16 in the verkex Chik) =(3,-16) so the Verlex form is most useful in finding the vexley which can be compared with the genera Vertex form to get h and k values (f) the graph of the function is shown below

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