Math Problem Statement

write the standard form. identify a,b,and c y=-(x+5)^2+9

Solution

To write the equation y=(x+5)2+9y = -(x+5)^2 + 9 in standard form, we first expand the equation.

Step 1: Expand (x+5)2(x+5)^2

(x+5)2=x2+10x+25(x+5)^2 = x^2 + 10x + 25

Step 2: Substitute into the equation

y=(x2+10x+25)+9y = -(x^2 + 10x + 25) + 9

Step 3: Distribute the negative sign

y=x210x25+9y = -x^2 - 10x - 25 + 9

Step 4: Combine like terms

y=x210x16y = -x^2 - 10x - 16

Thus, the standard form of the equation is: y=x210x16y = -x^2 - 10x - 16

Identifying the coefficients aa, bb, and cc:

  • a=1a = -1
  • b=10b = -10
  • c=16c = -16

Would you like more details on this process or have any questions?

Here are 5 related questions:

  1. How do you graph a quadratic equation in standard form?
  2. What does the value of aa tell us about the graph's direction?
  3. How do you find the vertex of a quadratic equation?
  4. What is the difference between standard and vertex form of a quadratic equation?
  5. How do you find the axis of symmetry for this equation?

Tip: The value of aa in a quadratic equation determines whether the parabola opens upward (a>0a > 0) or downward (a<0a < 0).

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Standard Form

Formulas

Standard form of a quadratic equation: y = ax^2 + bx + c

Theorems

Quadratic equation standard form theorem

Suitable Grade Level

Grades 9-10