Can I please receive help my math homework please thanks

Question

1.) Identify the matrix transformation of ΔDEF, which has coordinates D(3, −2),E(4, 1), and F(7, 2), for a translation 1 unit left and 2 units up. Then identify the correct vertices of the image.

A.)

 

B.) 

 

C.) 

 

D.) 

2.) Identify the zeros of the function g(x) = 4x2 + 8x + 7 using the Quadratic Formula.

 

A.) 

 

B.)

 

C.)

 

D.)

hello can you please solve and explain thanks

Answer 1

Hi Daniel D.,

For D(3, -2), E(4, 1), and F(7, 2), to translate left 1 unit and up 2 units you need to subtract 1 from the x-values and add 2 to the y-values.

So D'(3-1, -2+2), E'(4-1, 1+2), and F(7-1, 2+2), then D'(2, 0), E'(3, 3), and F'(6, 4). This is choice B, and maybe you can see now how the matrices work. Row1Column1 of the first matrix is added to Row1Column1 of the second matrix to equal Row1Column1 of the third matrix, and so on and so forth.

For g(x) = 4x² + 8x + 7 to find the x-intercepts we set g(x) = 0 (because when g(x) = 0, y-values are zero, and we are on the x-axis) and use the quadratic formula to solve. The quadratic formula is, x = [-b ± √(b² - 4ac)]/2a, for solving the equation ax² + bx +c = 0 and find the x-intercepts.

With a=2, b =8, and c=7;

x = [-8 ± √(8² - 4(4)(7))]/2(4)

x = [-8 ± √(64 - 112)]/8

x = [-8 ± √(-48)]/8

x = [-8 ± 4i√(3)]/8

x = -1 ± i√(3)/2 (answer A)

I hope this helps, Joe.