Math Problem Statement

Copy and complete the table of values for y = x^2 + 4x - 2. What numbers replace A, B, and C?

Solution

We are given the equation y=x2+4x−2y = x^2 + 4x - 2 and a table with different values of xx. We need to compute the corresponding values of yy to determine the missing entries AA, BB, and CC.

Step-by-Step Calculation:

  1. For x=−3x = -3: y=(−3)2+4(−3)−2=9−12−2=−5y = (-3)^2 + 4(-3) - 2 = 9 - 12 - 2 = -5 Therefore, A=−5A = -5.

  2. For x=0x = 0: y=(0)2+4(0)−2=0+0−2=−2y = (0)^2 + 4(0) - 2 = 0 + 0 - 2 = -2 Therefore, B=−2B = -2.

  3. For x=1x = 1: y=(1)2+4(1)−2=1+4−2=3y = (1)^2 + 4(1) - 2 = 1 + 4 - 2 = 3 Therefore, C=3C = 3.

Completed Table:

x & -3 & -2 & -1 & 0 & 1 \\ \hline y & -5 & -6 & -5 & -2 & 3 \\ \end{array}$$ Thus: - $$A = -5$$ - $$B = -2$$ - $$C = 3$$ Would you like any further details or explanations? ### Relative Questions: 1. How do you determine the vertex of the quadratic function $$y = x^2 + 4x - 2$$? 2. What is the axis of symmetry for the parabola given by $$y = x^2 + 4x - 2$$? 3. How can you graph the function $$y = x^2 + 4x - 2$$ using the points in the table? 4. What is the minimum or maximum value of the function $$y = x^2 + 4x - 2$$? 5. How would the function $$y = x^2 + 4x - 2$$ change if the constant term were increased by 3? ### Tip: To find the axis of symmetry for a quadratic equation $$y = ax^2 + bx + c$$, use the formula $$x = -\frac{b}{2a}$$.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Function Tables

Formulas

y = ax^2 + bx + c
Substitution for specific x-values

Theorems

Quadratic Function Properties

Suitable Grade Level

Grades 8-10

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