The Quadratic Formula Instruction & Assignment (EDGE 100%)
Complete the statements. Graph has one real root. Graph has a negative discriminant. Graph has an equation with coefficients a = 1, b = 4, c = -2
B A C
Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is
Positive Zero Negative
Is the solution shown below correct? Explain. 9x+2=8x2+6x
Sample Response/Explanation: No. The correct values of a, b, and c were substituted in, but the formula was simplified wrong. The 64 should be added so the radicand is 73. There should be 2 real roots.
Which of the statements about the following quadratic equation is true? 6x2 - 8 = 4x2 + 7x
a
Use the discriminant to answer the questions. 32x - 4 = 4x2 + 60For the equation shown, choose the description of the solutions. y - 5 = 0.5x2 + 6x - 3How many x-intercepts does the graph of this quadratic have?
a a
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equationh = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
b
Choose the equation that represents the solutions of 0 = 0.25x2 - 8x.
c
Solve 0 = 4x2+12x+9. Select the equation that shows the correct substitution of a, b, and c in the quadratic formula. Simplify the expression to solve the equation.
c -1.5
Given y = (2x + 3)2, choose the standard form of the given quadratic equation. Identify the values of a, b, and c.
d 4 12 9
Solve each of the quadratic equations. 3x = 0.5x2 0 = 5x2 - 2x + 6
d c
Determine the number of real solutions each quadratic equation has. y = 12x2 - 9x + 4 10x + y = -x2 + 2 4y - 7 = 5x2 - x + 2 + 3y y = (-x + 4)2
no two no one
Fill in the missing steps for the derivation of the quadratic formula using the choices below. Step 1: ax2 + bx + c = 0 Step 2: ax2 + bx = −c Step 3: Step 4:-------------- Step 5: Step 6: Step 7:-------------- Step 8:
step 3: B step 5: D step 6: A step 8: C
