The parabola in the graph below has a vertex at which point?
A(-1, 2)
B(1, -2)
C(2, 1)
D(0, 0)
Explanation
The vertex is the lowest point of an upward-opening parabola, marked at approximately (1, -2).
Question 2 of 20
Florida standards 2A-2HEasy Calc Word Diagram
What is the slope of the line shown?
A1/2
B2
C−1
D1
Explanation
📌 slope = rise/run = (2-(-2))/(2-(-2)) = 4/4 = 1
💡 Positive slope → line goes UP from left to right.
Question 3 of 20
Florida standards 5A-5CMedium Calc
Solve: 3x+4y=10, 2x−4y=−5
A(1, 2)
B(1, 1.75)
C(2, 1)
D(0, 2.5)
Explanation
📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75
Question 4 of 20
Florida standards 6A-6CEasy Calc Word
Complete the square: x² + 6x + ___ = (x + ___)²
A9, 3
B6, 3
C3, 9
D36, 6
Explanation
📌 Half of 6 = 3. Square it = 9. x² + 6x + 9 = (x + 3)²
Question 5 of 20
Florida standards 5A-5CMedium Calc Word Diagram
The system of equations is graphed below. How many solutions does it have?
ATwo solutions
BNo solution
CInfinitely many 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 6 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?
AOnly x = −8, because squaring a negative gives a positive
Bx = ±8 algebraically; the garden's side length is +8 ft
Cx = 32, because half of 64 is the side length
DOnly x = 8 — that's the only solution to x² = 64
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 7 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?
A3 sec
B2 sec
C1 sec
D4 sec
Explanation
📌 h = 0: −16t² + 48t = 0 → t(−16t + 48) = 0 → t = 0 or t = 3 seconds
Question 8 of 20
Florida standards 6A-6CMedium Calc Word
Use the quadratic formula for x² − 4x + 3 = 0
Ax = 1, 3
Bx = −1, −3
Cx = 2, 4
Dx = 0, 4
Explanation
📌 a=1, b=−4, c=3. x = (4 ± √(16−12))/2 = (4±2)/2 → x=3 or x=1
Question 9 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?
ANo real solutions — the parabola doesn't reach the x-axis
BTwo real solutions — the parabola crosses the x-axis twice
CThe number of solutions can't be determined from D alone
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 10 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?
ANegative correlation
BPositive correlation
CCannot determine
DNo 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 11 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 = 30t + 0.10
BC = 0.10(30 + t)
CC = 30.10t
DC = 30 + 0.10t
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 12 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?