Math Problem Statement

Copy and complete the table of values for y = x^2 + 4x - 3. What numbers replace A, B, and C?

Solution

The function given is:

y=x2+4x−3y = x^2 + 4x - 3

We need to compute the values of yy corresponding to the given xx values for the table.

Step 1: Compute AA when x=−3x = -3

Substitute x=−3x = -3 into the equation:

y=(−3)2+4(−3)−3=9−12−3=−6y = (-3)^2 + 4(-3) - 3 = 9 - 12 - 3 = -6

So, A=−6A = -6.

Step 2: Compute BB when x=0x = 0

Substitute x=0x = 0 into the equation:

y=(0)2+4(0)−3=−3y = (0)^2 + 4(0) - 3 = -3

So, B=−3B = -3.

Step 3: Compute CC when x=1x = 1

Substitute x=1x = 1 into the equation:

y=(1)2+4(1)−3=1+4−3=2y = (1)^2 + 4(1) - 3 = 1 + 4 - 3 = 2

So, C=2C = 2.

Final Table:

x & -3 & -2 & -1 & 0 & 1 \\ \hline y & -6 & -7 & -6 & -3 & 2 \\ \end{array}$$ Let me know if you'd like further clarification or more details! Here are some related questions: 1. How do we calculate $$y$$ for other values of $$x$$? 2. What does the graph of $$y = x^2 + 4x - 3$$ look like? 3. Can we factor the quadratic expression $$x^2 + 4x - 3$$? 4. How can we determine the vertex of the parabola for this equation? 5. What is the significance of the discriminant for this quadratic equation? **Tip:** Always substitute values carefully and double-check arithmetic steps when working with quadratic equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Function Evaluation

Formulas

Quadratic function y = x^2 + bx + c
y = x^2 + 4x - 3

Theorems

Evaluation of a quadratic function by substitution

Suitable Grade Level

Grades 7-9

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