📌 Half of 6 = 3. Square it = 9. x² + 6x + 9 = (x + 3)²
Question 2 of 10
Florida standards 5A-5CMedium Calc Word Diagram
The graph shows two lines. What is the solution to the system?
A(2, 3)
B(3, 0)
C(1, 2)
D(0, 1)
Explanation
📌 The solution is where the lines intersect = (1, 2). Verify: y = x + 1 → 2 = 1 + 1 ✓ y = −x + 3 → 2 = −1 + 3 ✓
Question 3 of 10
Florida standards 6A-6CHard Calc Word
Use quadratic formula: 2x²−5x−3=0
Ax=−3 or x=1/2
Bx=2 or x=−3
Cx=3 or x=−1/2
Dx=5 or x=−3
Explanation
📌 x=(5±√(25+24))/4=(5±7)/4. x=3 or x=−1/2
Question 4 of 10
Florida standards 1A-1GMedium Calc Word
A car rental costs $25 per day plus $0.15 per mile. If the total cost is $70 for one day, how many miles were driven?
A250
B300
C200
D350
Explanation
📌 70 = 25 + 0.15m 45 = 0.15m m = 300 miles
Question 5 of 10
Florida standards 8A-8BMedium Calc Diagram
For a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac. It tells us how many times the related parabola y = ax² + bx + c crosses the x-axis — and therefore how many real solutions the equation has.
The discriminant's sign matches the number of x-axis crossings.
Which statement about D = 0 is TRUE?
ATwo real solutions — the parabola crosses the x-axis twice
BThe number of solutions can't be determined from D alone
CNo real solutions — the parabola doesn't reach the x-axis
DExactly one real solution — the parabola is tangent to the x-axis
Explanation
The discriminant b² − 4ac counts how many real solutions a quadratic equation has by reflecting how many times the parabola y = ax² + bx + c crosses the x-axis.
The three cases: • D > 0: parabola crosses the x-axis at TWO different points → 2 real solutions. • D = 0: parabola is *tangent* to the x-axis — it touches at exactly ONE point (the vertex itself sits on the x-axis) → 1 real solution (often called a *double root*). • D < 0: parabola sits entirely above or below the x-axis, never touching it → 0 real solutions (the roots are complex / imaginary).
Application: D = 0 is the borderline case useful for problems like "for what value of c does ax² + bx + c = 0 have exactly one solution?" — set b² − 4ac = 0 and solve.
Question 6 of 10
Florida standards 5A-5CHard Calc
Solve: 3x+4y=10, 2x−4y=−5
A(1, 2)
B(2, 1)
C(1, 1.75)
D(0, 2.5)
Explanation
📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75
Question 7 of 10
Florida standards 2A-2HMedium Calc Word Diagram
Which line has a negative slope?
AA
BBoth
CB
DNeither
Explanation
📌 Negative slope = line goes DOWN from left to right (↘). Positive slope = line goes UP from left to right (↗). Graph B has negative slope.
Question 8 of 10
Florida standards 1A-1GMedium Calc Word
A ball is thrown upward. Its height is h = −16t² + 48t. When does it hit the ground?
A3 sec
B1 sec
C4 sec
D2 sec
Explanation
📌 h = 0: −16t² + 48t = 0 → t(−16t + 48) = 0 → t = 0 or t = 3 seconds
Question 9 of 10
Florida standards 5A-5CHard Calc Word
Solve: 2x + 3y = 13, 4x − y = 5
A(4, 1)
B(3, 2)
C(2, 3)
D(1, 4)
Explanation
📌 From eq2: y = 4x − 5 Substitute: 2x + 3(4x−5) = 13 → 2x + 12x − 15 = 13 → 14x = 28 → x = 2 y = 4(2) − 5 = 3
Question 10 of 10
Florida standards 7A-7CEasy Calc Word Diagram
Which graph represents a quadratic function?
AA
BBoth
CB
DNeither
Explanation
📌 Quadratic = U-shaped parabola. Graph A shows a parabola. Graph B is a straight line → linear, not quadratic.