4.7 Quadratic Formula

Solve each equation using the quadratic formula:

 $2x^2+11x=40$  

•  $\left\{-\frac{5}{2},\ 8\right\}$  

•  $\left\{-\frac{23}{4},-\frac{65}{4}\right\}$  

•  $\left\{\frac{23}{4},\ \frac{65}{4}\right\}$  

•  $\left\{\frac{5}{2},-8\right\}$  

Solve each equation using the quadratic formula:

 $5x^2-10x=2$  

•  $x=1\pm2\sqrt{35}$  

•  $x=1\pm\sqrt{35}$  

•  $x=1\pm\sqrt{7}$  

•  $x=\frac{5\pm\sqrt{35}}{5}$  

Tags

CCSS.HSA-REI.B.4B

Solve each equation using the quadratic formula:

 $5x^2+8x+3=6x^2-4x$  

•  $x=6\pm\sqrt{39}$  

•  $x=\frac{-4\pm5i}{22}$  

•  $x=-\frac{2}{11},\ x=5$  

•  $x=-6\pm2\sqrt{39}$  

Tags

CCSS.HSA-REI.B.4B

Solve each equation using the quadratic formula:

 $-3x^2-9x+8=-4$  

•  $\left\{\frac{13}{2},\ \frac{23}{2}\right\}$  

•  $x=-\frac{9\pm\sqrt{129}}{6}$  

•  $x=\frac{-3\pm\sqrt{7}}{2}$  

•  $\left\{-4,\ 1\right\}$  

Use the quadratic formula to solve 2x² + 2x - 12 = 0

• {-2, 3}

• {2, 3}

• {2, -3}

• {-2, -3}

Use the quadratic formula to solve x² - 4x + 3 = 0

• {1, 3}

• {2, 3}

• {3, 3}

• {-1, -3}

If the graph of a quadratic does not intercept the x-axis at any point, then it has:

• 1 Real Solution
• 2 Real Solutions
• Half a Solution
• No Real Solution

Tags

CCSS.HSF-IF.C.7A

Use the discriminant to determine the number of solutions for x² + 4x + 5

• one solution

• two solutions

• no real solutions

Tags

CCSS.HSA-REI.B.4B

Use the discriminant to determine the number of solutions for x² - 4x - 5

• one solution

• two solutions

• no real solutions

Tags

CCSS.HSA-REI.B.4B

Use the discriminant to determine the number of solutions for -4x² + 20x - 25

• one solution

• two solutions

• no real solutions

Tags

CCSS.HSA-REI.B.4B