📌 Quadratic = U-shaped parabola. Graph A shows a parabola. Graph B is a straight line → linear, not quadratic.
Question 2 of 20
Florida standards 7A-7CEasy Calc Word
The vertex of y = (x − 3)² + 2 is:
A(3, 2)
B(−3, 2)
C(3, −2)
D(2, 3)
Explanation
📌 Vertex form: y = a(x−h)² + k. Vertex = (h, k) = (3, 2).
Question 3 of 20
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?
A350
B200
C250
D300
Explanation
📌 70 = 25 + 0.15m 45 = 0.15m m = 300 miles
Question 4 of 20
Florida standards 1A-1GEasy Calc
A square garden has an area of 64 square feet. If the side length is x feet, the relationship is x² = 64.
The algebra gives two mathematical solutions, but only one makes physical sense as a side length. Which choice gives BOTH algebraic solutions AND correctly identifies the physical side length?
Ax = 32, because half of 64 is the side length
Bx = ±8 algebraically; the garden's side length is +8 ft
COnly x = 8 — that's the only solution to x² = 64
DOnly x = −8, because squaring a negative gives a positive
Explanation
Taking the square root of both sides gives x = ±√64 = ±8, because both (+8)² = 64 AND (−8)² = 64. In pure algebra you must report both roots. For the physical garden, length can't be negative, so only +8 ft applies in context — but the algebraic answer set is {−8, +8}.
Common mistakes: (A) Dropping the negative root entirely. (D) Dividing 64 by 2 instead of taking a square root.
Tip: when you see x² = N, always write x = ±√N first, then decide which roots fit the real-world context.
Question 5 of 20
Florida standards 6A-6CEasy Calc Word
Complete the square: x² + 6x + ___ = (x + ___)²
A9, 3
B36, 6
C3, 9
D6, 3
Explanation
📌 Half of 6 = 3. Square it = 9. x² + 6x + 9 = (x + 3)²
Question 6 of 20
Florida standards 4A-4CEasy Calc Word Diagram
The scatter plot shows the relationship between hours studied and test scores. What type of correlation is shown?
ACannot determine
BNo correlation
CPositive correlation
DNegative correlation
Explanation
📌 Points trend upward from left to right → positive correlation. As hours studied increases, test score increases. The trend line slopes upward → positive relationship.
Question 7 of 20
Florida standards 1A-1GEasy Calc Word Diagram
A cell phone plan charges $30 per month plus $0.10 per text. Which equation represents the monthly cost C for t texts?
AC = 30 + 0.10t
BC = 30.10t
CC = 30t + 0.10
DC = 0.10(30 + t)
Explanation
📌 Fixed cost = $30 (base monthly charge) Variable cost = $0.10 per text = 0.10t Total: C = 30 + 0.10t
💡 This is a linear equation in slope-intercept form: y = mx + b where m = 0.10 and b = 30.
Question 8 of 20
Florida standards 5A-5CMedium Calc Word
Solve: 2x + 3y = 13, 4x − y = 5
A(4, 1)
B(3, 2)
C(1, 4)
D(2, 3)
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 9 of 20
Florida standards 6A-6CMedium Calc Word
Use quadratic formula: 2x²−5x−3=0
Ax=2 or x=−3
Bx=−3 or x=1/2
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 10 of 20
Florida standards 5A-5CMedium Calc Word Diagram
The system of equations is graphed below. How many solutions does it have?
ANo solution
BInfinitely many solutions
CTwo solutions
DOne solution
Explanation
📌 The lines are parallel (same slope, different y-intercepts). Parallel lines NEVER intersect → NO solution.
Systems with no solution are called 'inconsistent.'
Question 11 of 20
Florida standards 6A-6CEasy Calc
Factor: x² + 5x + 6
A(x+2)(x+3)
B(x+3)(x+3)
C(x−2)(x−3)
D(x+1)(x+6)
Explanation
📌 Find two numbers that multiply to 6 and add to 5: 2 and 3. (x + 2)(x + 3)
💡 Positive slope → line goes UP from left to right.
Question 15 of 20
Florida standards 1A-1GMedium Calc Word
A ball is thrown upward. Its height is h = −16t² + 48t. When does it hit the ground?
A4 sec
B1 sec
C2 sec
D3 sec
Explanation
📌 h = 0: −16t² + 48t = 0 → t(−16t + 48) = 0 → t = 0 or t = 3 seconds
Question 16 of 20
Florida standards 5A-5CMedium Calc Word Diagram
The graph shows two lines. What is the solution to the system?
A(2, 3)
B(1, 2)
C(3, 0)
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 17 of 20
Florida standards 2A-2HEasy Calc Word Diagram
Which line has a negative slope?
AB
BA
CNeither
DBoth
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 18 of 20
Florida standards 8A-8BEasy 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?
AThe number of solutions can't be determined from D alone
BNo real solutions — the parabola doesn't reach the x-axis
CExactly one real solution — the parabola is tangent to the x-axis
DTwo real solutions — the parabola crosses the x-axis twice
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 19 of 20
Florida standards 6A-6CMedium Calc Word
Use the quadratic formula for x² − 4x + 3 = 0
Ax = −1, −3
Bx = 0, 4
Cx = 2, 4
Dx = 1, 3
Explanation
📌 a=1, b=−4, c=3. x = (4 ± √(16−12))/2 = (4±2)/2 → x=3 or x=1
Question 20 of 20
Florida standards 6A-6CEasy Calc Word Diagram
The parabola in the graph below has a vertex at which point?
A(-1, 2)
B(0, 0)
C(2, 1)
D(1, -2)
Explanation
The vertex is the lowest point of an upward-opening parabola, marked at approximately (1, -2).