The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) are the coordinates of the vertex.

Since the vertex of this parabola is (2, -3), we can plug in these values into the vertex form:

f(x) = a(x - 2)² - 3

To find f(0), we can plug in x = 0:

f(0) = a(0 - 2)² - 3
f(0) = a(-2)² - 3
f(0) = 4a - 3

The expression for f(0) is 4a - 3, which corresponds to option B.

To simplify the expression (3x² - 2x + 4) + (2x² + x - 3), we need to combine like terms:

(3x² - 2x + 4) + (2x² + x - 3)

3x² + 2x² - 2x + x + 4 - 3

5x² - x + 1

Thus, the simplified expression is 5x² - x + 1, which corresponds to option B.

To solve the inequality 4x - 3 < 2x + 5, we will isolate the variable x: Step 1: Subtract 2x from both sides of the inequality 2x - 3 < 5 Step 2: Add 3 to both sides of the inequality 2x < 8 Step 3: Divide by 2 x < 4 Thus, the inequality 4x - 3 < 2x + 5 is true for all values of x less than 4, which corresponds to option A.

To solve the system of linear equations, we can use either the substitution method or the elimination method. In this case, we'll use the elimination method since the second equation is already in the form of x - y.

Step 1: Add the two equations to eliminate y:
2x + y = 8
x - y = 4
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3x = 12

Step 2: Divide by 3 to solve for x:
x = 4

Step 3: Substitute x into the first equation:
2(4) + y = 8
y = 8 - 8
y = 0

Thus, the solution to the system of linear equations is x = 4 and y = 0, which corresponds to option A.

To solve the absolute value equation |3x - 4| = 8, we need to split the equation into two separate equations:

3x - 4 = 8 and 3x - 4 = -8

For the first equation, add 4 to both sides:
3x = 12
Divide by 3:
x = 4

For the second equation, add 4 to both sides:
3x = -4
Divide by 3:
x = -4/3

Thus, the solution to the absolute value equation |3x - 4| = 8 is x = 4 and x = -4/3, which corresponds to option D.