Question

1. 0/4 points | Previous Answers WaneFMAC7 2.1.009. Sketch the graph of the quadratic function. HINT (See Example 1.) f(x) = -x2 + 4x - 4 Tools Actions ROD Object Properties Select a tool or object to Begin Help WebAssign graphing tool Indicate the coordinates of the vertex, the y-intercept and the x intercepts (if any). (Il vertex (x, y)-( y-intercept x-intercept(s) Need Help? Read Submit Answer Price Another Version Viewing Saved Work Reverf to Last Response

Answer 1

Step 1 is to solve the equation for its roots:

• $-x^{2} + 4x -4 = 0$

• So the coefficients a , b and c are a=1,b=−4,c=4

• We use the quadratic formula to solve for the roots:

  • $x_{1,2} = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

  • $x_{1,2} = \frac{ -(-4) \pm \sqrt{ (-4)^2 - 4 \cdot 1 \cdot 4} }{ 2 \cdot 1 }$

  • $x_{1,2} = \frac{ 4 \pm \sqrt{ 0 } }{ 2 }$

  • $x_{1,2} = 2$

  • As at x = 2, the equation = 0, so the x intercept is (2,0)

  • Further, vertex is the minimum or the maximum point of the equation and is same as the x intercept

• Now the y intercept is the value of the equation if x = 0

  • $f(x) = -x^2+4x-4$

  • $f({0}) = -1 \cdot {0}^2 + 4 \cdot {0} - 4 = -4$

  • Therefore y intercept is (0, -4)

• Graph is as shown below:

• 

  f(x)-24x - 4 2 4 -1 -2 -3 -4 Y-inter -5 L

$%u2212x^{2} + 4x %u2212 4 = 0$