University:
High School
Course:
High School Mathematics
Academic year:

2021
Views:

144

Pages:

7
Author:

Marianna B

Name: Date: Solving Quadratic Equations using the Quadratic Formula You can find the solutions to any quadratic equation in standard form (ax 2 +bx+ c) using The Quadratic Formula. ✓ 2 -b+ b -4ac x=-------2a Ex 1: Solve 2x -5x + 3 = 0 2 using the quadratic formula. Identify a, b, and c. X-=- -(-5) .± ✓(-5) 2 -4CL)C7) Substitute those values into the Quadratic Formula 2(2-) }(:: 5' ±. -fi '7 - £;Y- x� 5± I - y 1 {p - 3 X-= 5+.-- ---y y 1. Simplify inside the radical. Be sure to follow order of operations! Evaluate the square root. Reduce the fractions if possible. Identify both solutions Determining the number of solutions using the discriminant Name: _________________________________ Date: _________________________________ The expression under the radical in the Quadratic Formula, is called the discriminant. b  b 2  4ac x 2a The Discriminant Interpreting the discriminant b 2  4ac  0   Two real solutions Two x-intercepts b 2  4ac  0   One real solution One x-intercept b 2  4ac  0   No real solutions No x-intercepts Determine the number of real solutions for each quadratic equation. Ex 1: x 2  8 x  3  0 Identify a, b, and c. Substitute those values into the discriminant of the Quadratic Equation Simplify. Be sure to follow order of operations! Determine the number of solutions (x-intercepts). b 2  4ac  0 Two solutions (two x-intercepts) b 2  4ac  0 One solution (one x-intercept) b 2  4ac  0 No solutions (no x-intercepts)